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calculus</title> <meta name="description" content="Search results for: Fractional calculus"> <meta name="keywords" content="Fractional calculus"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">164</span> Some Remarks About Riemann-Liouville and Caputo Impulsive Fractional Calculus</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20De%20la%20Sen">M. De la Sen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper establishes some closed formulas for Riemann- Liouville impulsive fractional integral calculus and also for Riemann- Liouville and Caputo impulsive fractional derivatives. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Rimann-%20Liouville%20fractional%20calculus" title="Rimann- Liouville fractional calculus">Rimann- Liouville fractional calculus</a>, <a href="https://publications.waset.org/search?q=Caputofractional%20derivative" title=" Caputofractional derivative"> Caputofractional derivative</a>, <a href="https://publications.waset.org/search?q=Dirac%20delta" title=" Dirac delta"> Dirac delta</a>, <a href="https://publications.waset.org/search?q=Distributional%20derivatives" title=" Distributional derivatives"> Distributional derivatives</a>, <a href="https://publications.waset.org/search?q=Highorderdistributional%20derivatives." title=" Highorderdistributional derivatives."> Highorderdistributional derivatives.</a> </p> <a href="https://publications.waset.org/9157/some-remarks-about-riemann-liouville-and-caputo-impulsive-fractional-calculus" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9157/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9157/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9157/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9157/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9157/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9157/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9157/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9157/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9157/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9157/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9157.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1425</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">163</span> Fractional-Order PI Controller Tuning Rules for Cascade Control System </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Truong%20Nguyen%20Luan%20Vu">Truong Nguyen Luan Vu</a>, <a href="https://publications.waset.org/search?q=Le%20Hieu%20Giang"> Le Hieu Giang</a>, <a href="https://publications.waset.org/search?q=Le%20Linh"> Le Linh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%E2%80%93order%20proportional%20integral%20controller" title=" fractional–order proportional integral controller"> fractional–order proportional integral controller</a>, <a href="https://publications.waset.org/search?q=cascade%20control%20system" title=" cascade control system"> cascade control system</a>, <a href="https://publications.waset.org/search?q=internal%20model%20control%20approach." title=" internal model control approach."> internal model control approach.</a> </p> <a href="https://publications.waset.org/10004885/fractional-order-pi-controller-tuning-rules-for-cascade-control-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10004885/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10004885/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10004885/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10004885/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10004885/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10004885/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10004885/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10004885/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10004885/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10004885/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10004885.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1557</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">162</span> Riemann-Liouville Fractional Calculus and Multiindex Dzrbashjan-Gelfond-Leontiev Differentiation and Integration with Multiindex Mittag-Leffler Function</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=U.K.%20Saha">U.K. Saha</a>, <a href="https://publications.waset.org/search?q=L.K.%20Arora"> L.K. Arora</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Multiindex%20Mittag-Leffler%20function" title="Multiindex Mittag-Leffler function">Multiindex Mittag-Leffler function</a>, <a href="https://publications.waset.org/search?q=Multiindex%20Dzrbashjan-Gelfond-Leontiev%20differentiation%20and%20integration" title=" Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration"> Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20integrals%20and%20derivatives." title=" Riemann-Liouville fractional integrals and derivatives."> Riemann-Liouville fractional integrals and derivatives.</a> </p> <a href="https://publications.waset.org/15470/riemann-liouville-fractional-calculus-and-multiindex-dzrbashjan-gelfond-leontiev-differentiation-and-integration-with-multiindex-mittag-leffler-function" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15470/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15470/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15470/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15470/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15470/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15470/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15470/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15470/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15470/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15470/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15470.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1531</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">161</span> Existence of Iterative Cauchy Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim">Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/search?q=Cauchy%20equation" title=" Cauchy equation"> Cauchy equation</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20operators" title=" Riemann-Liouville fractional operators"> Riemann-Liouville fractional operators</a>, <a href="https://publications.waset.org/search?q=Volterra%0D%0Aintegral%20equation" title=" Volterra integral equation"> Volterra integral equation</a>, <a href="https://publications.waset.org/search?q=non-expansive%20mapping" title=" non-expansive mapping"> non-expansive mapping</a>, <a href="https://publications.waset.org/search?q=iterative%20differential%20equation." title=" iterative differential equation."> iterative differential equation.</a> </p> <a href="https://publications.waset.org/17037/existence-of-iterative-cauchy-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/17037/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/17037/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/17037/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/17037/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/17037/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/17037/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/17037/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/17037/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/17037/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/17037/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/17037.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2684</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">160</span> A Mathematical Model Approach Regarding the Children’s Height Development with Fractional Calculus </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nisa%20%C3%96zge%20%C3%96nal">Nisa Özge Önal</a>, <a href="https://publications.waset.org/search?q=Kamil%20Kara%C3%A7uha"> Kamil Karaçuha</a>, <a href="https://publications.waset.org/search?q=G%C3%B6ksu%20Hazar%20Erdin%C3%A7"> Göksu Hazar Erdinç</a>, <a href="https://publications.waset.org/search?q=Banu%20Bahar%20Kara%C3%A7uha"> Banu Bahar Karaçuha</a>, <a href="https://publications.waset.org/search?q=Ertu%C4%9Frul%20Kara%C3%A7uha"> Ertuğrul Karaçuha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Children%20growth%20percentile" title="Children growth percentile">Children growth percentile</a>, <a href="https://publications.waset.org/search?q=children%20physical%20development" title=" children physical development"> children physical development</a>, <a href="https://publications.waset.org/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/search?q=linear%20and%20polynomial%20model." title=" linear and polynomial model. "> linear and polynomial model. </a> </p> <a href="https://publications.waset.org/10010402/a-mathematical-model-approach-regarding-the-childrens-height-development-with-fractional-calculus" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010402/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010402/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010402/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010402/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010402/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010402/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010402/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010402/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010402/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010402/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010402.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">860</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">159</span> Fractional Masks Based On Generalized Fractional Differential Operator for Image Denoising</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hamid%20A.%20Jalab">Hamid A. Jalab</a>, <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim"> Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper introduces an image denoising algorithm based on generalized Srivastava-Owa fractional differential operator for removing Gaussian noise in digital images. The structures of nxn fractional masks are constructed by this algorithm. Experiments show that, the capability of the denoising algorithm by fractional differential-based approach appears efficient to smooth the Gaussian noisy images for different noisy levels. The denoising performance is measured by using peak signal to noise ratio (PSNR) for the denoising images. The results showed an improved performance (higher PSNR values) when compared with standard Gaussian smoothing filter.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20operator" title=" fractional differential operator"> fractional differential operator</a>, <a href="https://publications.waset.org/search?q=fractional%20mask" title=" fractional mask"> fractional mask</a>, <a href="https://publications.waset.org/search?q=fractional%20filter." title=" fractional filter."> fractional filter.</a> </p> <a href="https://publications.waset.org/9996971/fractional-masks-based-on-generalized-fractional-differential-operator-for-image-denoising" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9996971/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9996971/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9996971/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9996971/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9996971/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9996971/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9996971/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9996971/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9996971/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9996971/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9996971.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3003</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">158</span> Fractional Order Feedback Control of a Ball and Beam System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Santosh%20Kr.%20Choudhary">Santosh Kr. Choudhary</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20order%20calculus" title="Fractional order calculus">Fractional order calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20order%20controller" title=" fractional order controller"> fractional order controller</a>, <a href="https://publications.waset.org/search?q=fractional%20order%20system" title=" fractional order system"> fractional order system</a>, <a href="https://publications.waset.org/search?q=ball%20and%20beam%20system" title=" ball and beam system"> ball and beam system</a>, <a href="https://publications.waset.org/search?q=PI%CE%BBD%CE%BC%20controller" title=" PIλDμ controller"> PIλDμ controller</a>, <a href="https://publications.waset.org/search?q=modelling" title=" modelling"> modelling</a>, <a href="https://publications.waset.org/search?q=simulation." title=" simulation."> simulation.</a> </p> <a href="https://publications.waset.org/9999009/fractional-order-feedback-control-of-a-ball-and-beam-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9999009/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9999009/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9999009/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9999009/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9999009/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9999009/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9999009/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9999009/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9999009/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9999009/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9999009.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3555</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">157</span> Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Elham%20Amini%20Boroujeni">Elham Amini Boroujeni</a>, <a href="https://publications.waset.org/search?q=Hamid%20Reza%20Momeni"> Hamid Reza Momeni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20order%20calculus" title="Fractional order calculus">Fractional order calculus</a>, <a href="https://publications.waset.org/search?q=Fractional%20order%20observer" title=" Fractional order observer"> Fractional order observer</a>, <a href="https://publications.waset.org/search?q=Linear%20matrix%20inequality" title=" Linear matrix inequality"> Linear matrix inequality</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20Systems" title=" Nonlinear Systems"> Nonlinear Systems</a>, <a href="https://publications.waset.org/search?q=Observer%20based%0AController." title=" Observer based Controller."> Observer based Controller.</a> </p> <a href="https://publications.waset.org/11187/observer-based-control-of-a-class-of-nonlinear-fractional-order-systems-using-lmi" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11187/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11187/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11187/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11187/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11187/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11187/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11187/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11187/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11187/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11187/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11187.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2880</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">156</span> Stability of Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim">Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/search?q=Lane-Emden%20equation" title=" Lane-Emden equation"> Lane-Emden equation</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20operators" title=" Riemann-Liouville fractional operators"> Riemann-Liouville fractional operators</a>, <a href="https://publications.waset.org/search?q=Volterra%20integral%20equation." title=" Volterra integral equation."> Volterra integral equation.</a> </p> <a href="https://publications.waset.org/16803/stability-of-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16803/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16803/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16803/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16803/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16803/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16803/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16803/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16803/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16803/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16803/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16803.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3717</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">155</span> Notes on Fractional k-Covered Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sizhong%20Zhou">Sizhong Zhou</a>, <a href="https://publications.waset.org/search?q=Yang%20Xu"> Yang Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A graph G is fractional k-covered if for each edge e of G, there exists a fractional k-factor h, such that h(e) = 1. If k = 2, then a fractional k-covered graph is called a fractional 2-covered graph. The binding number bind(G) is defined as follows, bind(G) = min{|NG(X)| |X| : ├ÿ = X Ôèå V (G),NG(X) = V (G)}. In this paper, it is proved that G is fractional 2-covered if δ(G) ≥ 4 and bind(G) > 5 3 . <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=graph" title="graph">graph</a>, <a href="https://publications.waset.org/search?q=binding%20number" title=" binding number"> binding number</a>, <a href="https://publications.waset.org/search?q=fractional%20k-factor" title=" fractional k-factor"> fractional k-factor</a>, <a href="https://publications.waset.org/search?q=fractional%20k-covered%20graph." title=" fractional k-covered graph."> fractional k-covered graph.</a> </p> <a href="https://publications.waset.org/15704/notes-on-fractional-k-covered-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15704/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15704/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15704/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15704/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15704/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15704/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15704/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15704/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15704/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15704/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15704.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1185</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">154</span> Application of a SubIval Numerical Solver for Fractional Circuits</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Marcin%20Sowa">Marcin Sowa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Numerical%20method" title="Numerical method">Numerical method</a>, <a href="https://publications.waset.org/search?q=SubIval" title=" SubIval"> SubIval</a>, <a href="https://publications.waset.org/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/search?q=numerical%20solver" title=" numerical solver"> numerical solver</a>, <a href="https://publications.waset.org/search?q=circuit%20analysis." title=" circuit analysis."> circuit analysis.</a> </p> <a href="https://publications.waset.org/10009391/application-of-a-subival-numerical-solver-for-fractional-circuits" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10009391/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10009391/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10009391/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10009391/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10009391/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10009391/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10009391/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10009391/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10009391/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10009391/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10009391.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">668</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">153</span> Use of Technology to Improve Students’ Attitude in Learning Mathematics of Non-Mathematics Undergraduate Students</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Asia%20Majeed">Asia Majeed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper will investigate a form of learning mathematics by integrating technology in mathematics specifically for the university first-year calculus class to support students’ engagement in learning which influences students' conceptual and procedural understanding of the calculus content in a better way. The students with good grades in high school calculus generally struggle in first-year university calculus classes in learning mathematical analysis concepts. This problem has to be addressed. If this problem is not resolved, then most likely students with less ability to do mathematics might not able to complete their degrees. In this work, MATLAB is used to help students in learning and in improving calculus concepts.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Calculus" title="Calculus">Calculus</a>, <a href="https://publications.waset.org/search?q=first-year%20university%20students" title=" first-year university students"> first-year university students</a>, <a href="https://publications.waset.org/search?q=teaching%20strategies" title=" teaching strategies"> teaching strategies</a>, <a href="https://publications.waset.org/search?q=MATLAB." title=" MATLAB."> MATLAB.</a> </p> <a href="https://publications.waset.org/10013035/use-of-technology-to-improve-students-attitude-in-learning-mathematics-of-non-mathematics-undergraduate-students" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10013035/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10013035/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10013035/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10013035/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10013035/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10013035/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10013035/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10013035/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10013035/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10013035/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10013035.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">397</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">152</span> On Fractional (k,m)-Deleted Graphs with Constrains Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sizhong%20Zhou">Sizhong Zhou</a>, <a href="https://publications.waset.org/search?q=Hongxia%20Liu"> Hongxia Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e&ni;x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Graph" title="Graph">Graph</a>, <a href="https://publications.waset.org/search?q=degree%20condition" title=" degree condition"> degree condition</a>, <a href="https://publications.waset.org/search?q=fractional%20k-factor" title=" fractional k-factor"> fractional k-factor</a>, <a href="https://publications.waset.org/search?q=fractional%20%28k" title=" fractional (k"> fractional (k</a>, <a href="https://publications.waset.org/search?q=m%29-deleted%20graph." title="m)-deleted graph.">m)-deleted graph.</a> </p> <a href="https://publications.waset.org/3345/on-fractional-km-deleted-graphs-with-constrains-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3345/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3345/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3345/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3345/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3345/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3345/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3345/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3345/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3345/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3345/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3345.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1200</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">151</span> Calculus-based Runtime Verification</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Xuan%20Qi">Xuan Qi</a>, <a href="https://publications.waset.org/search?q=Changzhi%20Zhao"> Changzhi Zhao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a uniform calculus-based approach for synthesizing monitors checking correctness properties specified by a large variety of logics at runtime is provided, including future and past time logics, interval logics, state machine and parameterized temporal logics. We present a calculus mechanism to synthesize monitors from the logical specification for the incremental analysis of execution traces during test and real run. The monitor detects both good and bad prefix of a particular kind, namely those that are informative for the property under investigation. We elaborate the procedure of calculus as monitors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=calculus" title="calculus">calculus</a>, <a href="https://publications.waset.org/search?q=eagle%20logic" title=" eagle logic"> eagle logic</a>, <a href="https://publications.waset.org/search?q=monitor%20synthesis" title=" monitor synthesis"> monitor synthesis</a>, <a href="https://publications.waset.org/search?q=runtime%20verification" title=" runtime verification"> runtime verification</a> </p> <a href="https://publications.waset.org/15100/calculus-based-runtime-verification" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15100/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15100/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15100/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15100/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15100/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15100/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15100/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15100/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15100/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15100/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15100.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1258</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">150</span> A Neighborhood Condition for Fractional k-deleted Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sizhong%20Zhou">Sizhong Zhou</a>, <a href="https://publications.waset.org/search?q=Hongxia%20Liu"> Hongxia Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Graph" title="Graph">Graph</a>, <a href="https://publications.waset.org/search?q=minimum%20degree" title=" minimum degree"> minimum degree</a>, <a href="https://publications.waset.org/search?q=neighborhood%20union" title=" neighborhood union"> neighborhood union</a>, <a href="https://publications.waset.org/search?q=fractional%20k-factor" title=" fractional k-factor"> fractional k-factor</a>, <a href="https://publications.waset.org/search?q=fractional%20k-deleted%20graph." title=" fractional k-deleted graph."> fractional k-deleted graph.</a> </p> <a href="https://publications.waset.org/4161/a-neighborhood-condition-for-fractional-k-deleted-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/4161/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/4161/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/4161/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/4161/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/4161/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/4161/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/4161/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/4161/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/4161/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/4161/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/4161.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1066</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">149</span> Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changhong%20Guo">Changhong Guo</a>, <a href="https://publications.waset.org/search?q=Shaomei%20Fang"> Shaomei Fang</a>, <a href="https://publications.waset.org/search?q=Yong%20He"> Yong He</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=European%20option%20pricing" title="European option pricing">European option pricing</a>, <a href="https://publications.waset.org/search?q=fractional%20Black-Scholes%0D%0Aequations" title=" fractional Black-Scholes equations"> fractional Black-Scholes equations</a>, <a href="https://publications.waset.org/search?q=fractional%20G-Brownian%20motion" title=" fractional G-Brownian motion"> fractional G-Brownian motion</a>, <a href="https://publications.waset.org/search?q=Taylor%E2%80%99s%20series%20of%20fractional%0D%0Aorder" title=" Taylor’s series of fractional order"> Taylor’s series of fractional order</a>, <a href="https://publications.waset.org/search?q=uncertain%20volatility." title=" uncertain volatility."> uncertain volatility.</a> </p> <a href="https://publications.waset.org/10011894/derivation-of-fractional-black-scholes-equations-driven-by-fractional-g-brownian-motion-and-their-application-in-european-option-pricing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10011894/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10011894/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10011894/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10011894/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10011894/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10011894/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10011894/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10011894/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10011894/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10011894/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10011894.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">858</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">148</span> Stability of Interval Fractional-order Systems with Order 0 < α < 1</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hong%20Li">Hong Li</a>, <a href="https://publications.waset.org/search?q=Shou-ming%20Zhong"> Shou-ming Zhong</a>, <a href="https://publications.waset.org/search?q=Hou-biao%20Li"> Hou-biao Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Interval%20fractional-order%20systems" title="Interval fractional-order systems">Interval fractional-order systems</a>, <a href="https://publications.waset.org/search?q=linear%20matrix%20inequality%20%28LMI%29" title=" linear matrix inequality (LMI)"> linear matrix inequality (LMI)</a>, <a href="https://publications.waset.org/search?q=asymptotical%20stability." title=" asymptotical stability."> asymptotical stability.</a> </p> <a href="https://publications.waset.org/1954/stability-of-interval-fractional-order-systems-with-order-0-a-1" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1954/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1954/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1954/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1954/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1954/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1954/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1954/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1954/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1954/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1954/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1954.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3615</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">147</span> Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ali%20Dorostkar">Ali Dorostkar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Tangent%20line" title="Tangent line">Tangent line</a>, <a href="https://publications.waset.org/search?q=fractional%20dimension" title=" fractional dimension"> fractional dimension</a>, <a href="https://publications.waset.org/search?q=root" title=" root"> root</a>, <a href="https://publications.waset.org/search?q=optimization%20problem." title=" optimization problem."> optimization problem.</a> </p> <a href="https://publications.waset.org/10010711/relation-between-roots-and-tangent-lines-of-function-in-fractional-dimensions-a-method-for-optimization-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010711/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010711/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010711/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010711/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010711/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010711/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010711/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010711/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010711/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010711/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010711.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">564</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">146</span> Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kazem%20Ghanbari">Kazem Ghanbari</a>, <a href="https://publications.waset.org/search?q=Yousef%20Gholami"> Yousef Gholami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20derivatives%20and%20integrals" title="Fractional derivatives and integrals">Fractional derivatives and integrals</a>, <a href="https://publications.waset.org/search?q=Hamiltonian%0D%0Asystem" title=" Hamiltonian system"> Hamiltonian system</a>, <a href="https://publications.waset.org/search?q=Lyapunov%20type%20inequalities" title=" Lyapunov type inequalities"> Lyapunov type inequalities</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=disconjugacy." title=" disconjugacy."> disconjugacy.</a> </p> <a href="https://publications.waset.org/10004599/lyapunov-type-inequalities-for-fractional-impulsive-hamiltonian-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10004599/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10004599/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10004599/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10004599/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10004599/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10004599/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10004599/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10004599/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10004599/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10004599/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10004599.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1526</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">145</span> Application of Fractional Model Predictive Control to Thermal System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Aymen%20Rhouma">Aymen Rhouma</a>, <a href="https://publications.waset.org/search?q=Khaled%20Hcheichi"> Khaled Hcheichi</a>, <a href="https://publications.waset.org/search?q=Sami%20Hafsi"> Sami Hafsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller<em>.</em></p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20model%20predictive%20control" title="Fractional model predictive control">Fractional model predictive control</a>, <a href="https://publications.waset.org/search?q=fractional%20order%20systems" title=" fractional order systems"> fractional order systems</a>, <a href="https://publications.waset.org/search?q=thermal%20system." title=" thermal system."> thermal system.</a> </p> <a href="https://publications.waset.org/10006816/application-of-fractional-model-predictive-control-to-thermal-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006816/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006816/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006816/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006816/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006816/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006816/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006816/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006816/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006816/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006816/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006816.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1226</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">144</span> Realization of Fractional-Order Capacitors with Field-Effect Transistors</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Steve%20Hung-Lung%20Tu">Steve Hung-Lung Tu</a>, <a href="https://publications.waset.org/search?q=Yu-Hsuan%20Cheng"> Yu-Hsuan Cheng</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A novel and efficient approach to realize fractional-order capacitors is investigated in this paper. Meanwhile, a new approach which is more efficient for semiconductor implementation of fractional-order capacitors is proposed. The feasibility of the approach has been verified with the preliminary measured results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional-order" title="Fractional-order">Fractional-order</a>, <a href="https://publications.waset.org/search?q=field-effect%20transistors" title=" field-effect transistors"> field-effect transistors</a>, <a href="https://publications.waset.org/search?q=RC%0Atransmission%20lines." title=" RC transmission lines."> RC transmission lines.</a> </p> <a href="https://publications.waset.org/13055/realization-of-fractional-order-capacitors-with-field-effect-transistors" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13055/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13055/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13055/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13055/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13055/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13055/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13055/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13055/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13055/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13055/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13055.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3162</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">143</span> A Design of Fractional-Order PI Controller with Error Compensation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Mazidah%20Tajjudin">Mazidah Tajjudin</a>, <a href="https://publications.waset.org/search?q=Norhashim%20Mohd%20Arshad"> Norhashim Mohd Arshad</a>, <a href="https://publications.waset.org/search?q=Ramli%20Adnan"> Ramli Adnan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional-order%20PI" title="Fractional-order PI">Fractional-order PI</a>, <a href="https://publications.waset.org/search?q=Ziegler-Nichols%20tuning" title=" Ziegler-Nichols tuning"> Ziegler-Nichols tuning</a>, <a href="https://publications.waset.org/search?q=Oustaloup%27s%20Recursive%20Approximation" title=" Oustaloup's Recursive Approximation"> Oustaloup's Recursive Approximation</a>, <a href="https://publications.waset.org/search?q=steam%20temperature%20control." title=" steam temperature control."> steam temperature control.</a> </p> <a href="https://publications.waset.org/5265/a-design-of-fractional-order-pi-controller-with-error-compensation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5265/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5265/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5265/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5265/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5265/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5265/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5265/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5265/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5265/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5265/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5265.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2300</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">142</span> The Boundary Element Method in Excel for Teaching Vector Calculus and Simulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Stephen%20Kirkup">Stephen Kirkup</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Boundary%20element%20method" title="Boundary element method">Boundary element method</a>, <a href="https://publications.waset.org/search?q=laplace%20equation" title=" laplace equation"> laplace equation</a>, <a href="https://publications.waset.org/search?q=vector%20calculus" title=" vector calculus"> vector calculus</a>, <a href="https://publications.waset.org/search?q=simulation" title=" simulation"> simulation</a>, <a href="https://publications.waset.org/search?q=education." title=" education."> education.</a> </p> <a href="https://publications.waset.org/10009857/the-boundary-element-method-in-excel-for-teaching-vector-calculus-and-simulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10009857/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10009857/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10009857/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10009857/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10009857/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10009857/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10009857/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10009857/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10009857/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10009857/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10009857.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">995</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">141</span> Oil Displacement by Water in Hauterivian Sandstone Reservoir of Kashkari Oil Field</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20J.%20Nazari">A. J. Nazari</a>, <a href="https://publications.waset.org/search?q=S.%20Honma"> S. Honma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper evaluates oil displacement by water in Hauterivian sandstone reservoir of Kashkari oil field in North of Afghanistan. The core samples of this oil field were taken out from well No-21<sup>st</sup>, and the relative permeability and fractional flow are analyzed. Steady state flow laboratory experiments are performed to empirically obtain the fractional flow curves and relative permeability in different water saturation ratio. The relative permeability represents the simultaneous flow behavior in the reservoir. The fractional flow approach describes the individual phases as fractional of the total flow. The fractional flow curve interprets oil displacement by water, and from the tangent of fractional flow curve can find out the average saturation behind the water front flow saturation. Therefore, relative permeability and fractional flow curves are suitable for describing the displacement of oil by water in a petroleum reservoir. The effects of irreducible water saturation, residual oil saturation on the displaceable amount of oil are investigated through Buckley-Leveret analysis.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20flow" title="Fractional flow">Fractional flow</a>, <a href="https://publications.waset.org/search?q=oil%20displacement" title=" oil displacement"> oil displacement</a>, <a href="https://publications.waset.org/search?q=relative%20permeability" title=" relative permeability"> relative permeability</a>, <a href="https://publications.waset.org/search?q=simultaneously%20flow." title=" simultaneously flow."> simultaneously flow.</a> </p> <a href="https://publications.waset.org/10006133/oil-displacement-by-water-in-hauterivian-sandstone-reservoir-of-kashkari-oil-field" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006133/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006133/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006133/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006133/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006133/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006133/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006133/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006133/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006133/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006133/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006133.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1311</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">140</span> An Efficient Hamiltonian for Discrete Fractional Fourier Transform</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sukrit%20Shankar">Sukrit Shankar</a>, <a href="https://publications.waset.org/search?q=Pardha%20Saradhi%20K."> Pardha Saradhi K.</a>, <a href="https://publications.waset.org/search?q=Chetana%20Shanta%20Patsa"> Chetana Shanta Patsa</a>, <a href="https://publications.waset.org/search?q=Jaydev%20Sharma"> Jaydev Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20Fourier%20Transform" title="Fractional Fourier Transform">Fractional Fourier Transform</a>, <a href="https://publications.waset.org/search?q=Hamiltonian" title=" Hamiltonian"> Hamiltonian</a>, <a href="https://publications.waset.org/search?q=Eigen%0AVectors" title=" Eigen Vectors"> Eigen Vectors</a>, <a href="https://publications.waset.org/search?q=Discrete%20Hermite%20Gaussians." title=" Discrete Hermite Gaussians."> Discrete Hermite Gaussians.</a> </p> <a href="https://publications.waset.org/10293/an-efficient-hamiltonian-for-discrete-fractional-fourier-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10293/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10293/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10293/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10293/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10293/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10293/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10293/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10293/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10293/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10293/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10293.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1529</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">139</span> Lower Bound of Time Span Product for a General Class of Signals in Fractional Fourier Domain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sukrit%20Shankar">Sukrit Shankar</a>, <a href="https://publications.waset.org/search?q=Chetana%20Shanta%20Patsa"> Chetana Shanta Patsa</a>, <a href="https://publications.waset.org/search?q=Jaydev%20Sharma"> Jaydev Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20Fourier%20Transform" title="Fractional Fourier Transform">Fractional Fourier Transform</a>, <a href="https://publications.waset.org/search?q=uncertainty%20principle" title=" uncertainty principle"> uncertainty principle</a>, <a href="https://publications.waset.org/search?q=Fractional%20Fourier%20Span" title=" Fractional Fourier Span"> Fractional Fourier Span</a>, <a href="https://publications.waset.org/search?q=amplitude" title=" amplitude"> amplitude</a>, <a href="https://publications.waset.org/search?q=phase." title=" phase."> phase.</a> </p> <a href="https://publications.waset.org/8228/lower-bound-of-time-span-product-for-a-general-class-of-signals-in-fractional-fourier-domain" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8228/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8228/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8228/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8228/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8228/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8228/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8228/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8228/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8228/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8228/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8228.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1192</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">138</span> Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Zarebnia">M. Zarebnia</a>, <a href="https://publications.waset.org/search?q=N.%20Aliniya"> N. Aliniya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a numerical solution based on sinc functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Calculus%20of%20variation%3B%20Sinc%20functions%3B%20Galerkin%3B%20Numerical%20method" title="Calculus of variation; Sinc functions; Galerkin; Numerical method">Calculus of variation; Sinc functions; Galerkin; Numerical method</a> </p> <a href="https://publications.waset.org/9998/sinc-galerkin-method-for-the-solution-of-problems-in-calculus-of-variations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9998/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9998/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9998/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9998/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9998/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9998/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9998/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9998/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9998/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9998/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9998.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1959</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">137</span> Non-Polynomial Spline Method for the Solution of Problems in Calculus of Variations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Zarebnia">M. Zarebnia</a>, <a href="https://publications.waset.org/search?q=M.%20Hoshyar"> M. Hoshyar</a>, <a href="https://publications.waset.org/search?q=M.%20Sedaghati"> M. Sedaghati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Calculus%20of%20variation%3B%20Non-polynomial%20spline%20functions%3B%20Numerical%20method" title="Calculus of variation; Non-polynomial spline functions; Numerical method">Calculus of variation; Non-polynomial spline functions; Numerical method</a> </p> <a href="https://publications.waset.org/6590/non-polynomial-spline-method-for-the-solution-of-problems-in-calculus-of-variations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6590/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6590/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6590/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6590/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6590/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6590/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6590/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6590/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6590/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6590/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6590.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1982</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">136</span> Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sukrit%20Shankar">Sukrit Shankar</a>, <a href="https://publications.waset.org/search?q=Chetana%20Shanta%20Patsa"> Chetana Shanta Patsa</a>, <a href="https://publications.waset.org/search?q=Jaydev%20Sharma"> Jaydev Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve better decorrelation of the windowed and overlapped time signal. We present an expression that is useful for finding the perturbation in the Fractional Fourier span due to the erroneous transform order and the possible variation in the window shape and length. The expression is based on the dependency of the time-Fractional Fourier span Uncertainty on the amplitude and phase function of the signal. We also show with the help of the developed expression that the perturbation of span has a varying degree of sensitivity for varying degree of transform order and the window coefficients. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20Fourier%20Transform" title="Fractional Fourier Transform">Fractional Fourier Transform</a>, <a href="https://publications.waset.org/search?q=Perturbation" title=" Perturbation"> Perturbation</a>, <a href="https://publications.waset.org/search?q=Fractional%20Fourier%20span" title="Fractional Fourier span">Fractional Fourier span</a>, <a href="https://publications.waset.org/search?q=amplitude" title=" amplitude"> amplitude</a>, <a href="https://publications.waset.org/search?q=phase" title=" phase"> phase</a>, <a href="https://publications.waset.org/search?q=transform%20order" title=" transform order"> transform order</a>, <a href="https://publications.waset.org/search?q=filterbanks." title=" filterbanks."> filterbanks.</a> </p> <a href="https://publications.waset.org/9355/perturbation-in-the-fractional-fourier-span-due-to-erroneous-transform-order-and-window-function" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9355/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9355/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9355/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9355/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9355/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9355/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9355/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9355/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9355/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9355/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9355.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1468</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">135</span> Quality Factor Variation with Transform Order in Fractional Fourier Domain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sukrit%20Shankar">Sukrit Shankar</a>, <a href="https://publications.waset.org/search?q=Chetana%20Shanta%20Patsa"> Chetana Shanta Patsa</a>, <a href="https://publications.waset.org/search?q=K.%20Pardha%20Saradhi"> K. Pardha Saradhi</a>, <a href="https://publications.waset.org/search?q=Jaydev%20Sharma"> Jaydev Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fractional Fourier Transform is a powerful tool, which is a generalization of the classical Fourier Transform. This paper provides a mathematical relation relating the span in Fractional Fourier domain with the amplitude and phase functions of the signal, which is further used to study the variation of quality factor with different values of the transform order. It is seen that with the increase in the number of transients in the signal, the deviation of average Fractional Fourier span from the frequency bandwidth increases. Also, with the increase in the transient nature of the signal, the optimum value of transform order can be estimated based on the quality factor variation, and this value is found to be very close to that for which one can obtain the most compact representation. With the entire mathematical analysis and experimentation, we consolidate the fact that Fractional Fourier Transform gives more optimal representations for a number of transform orders than Fourier transform. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20Fourier%20Transform" title="Fractional Fourier Transform">Fractional Fourier Transform</a>, <a href="https://publications.waset.org/search?q=Quality%20Factor" title=" Quality Factor"> Quality Factor</a>, <a href="https://publications.waset.org/search?q=Fractional%20Fourier%20span" title=" Fractional Fourier span"> Fractional Fourier span</a>, <a href="https://publications.waset.org/search?q=transient%20signals." title=" transient signals."> transient signals.</a> </p> <a href="https://publications.waset.org/9485/quality-factor-variation-with-transform-order-in-fractional-fourier-domain" class="btn btn-primary btn-sm">Procedia</a> <a 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