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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">3572</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">5929</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">2320</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">5928</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">2903</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">5927</span> PSO Based Optimal Design of Fractional Order Controller for Industrial Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rohit%20Gupta">Rohit Gupta</a>, <a href="https://publications.waset.org/search?q=Ruchika"> Ruchika</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a PSO based fractional order PID (FOPID) controller is proposed for concentration control of an isothermal Continuous Stirred Tank Reactor (CSTR) problem. CSTR is used to carry out chemical reactions in industries, which possesses complex nonlinear dynamic characteristics. Particle Swarm Optimization algorithm technique, which is an evolutionary optimization technique based on the movement and intelligence of swarm is proposed for tuning of the controller for this system. Comparisons of proposed controller with conventional and fuzzy based controller illustrate the superiority of proposed PSO-FOPID controller. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=CSTR" title="CSTR">CSTR</a>, <a href="https://publications.waset.org/search?q=Fractional%20Order%20PID%20Controller" title=" Fractional Order PID Controller"> Fractional Order PID Controller</a>, <a href="https://publications.waset.org/search?q=Partical%20Swarm%20Optimization." title=" Partical Swarm Optimization."> Partical Swarm Optimization.</a> </p> <a href="https://publications.waset.org/10003695/pso-based-optimal-design-of-fractional-order-controller-for-industrial-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10003695/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10003695/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10003695/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10003695/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10003695/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10003695/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10003695/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10003695/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10003695/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10003695/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10003695.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">1499</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">5926</span> Robust Fractional-Order PI Controller with Ziegler-Nichols Rules</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=Mohd%20Hezri%20Fazalul%20Rahiman"> Mohd Hezri Fazalul Rahiman</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>In process control applications, above 90% of the controllers are of PID type. This paper proposed a robust PI controller with fractional-order integrator. The PI parameters were obtained using classical Ziegler-Nichols rules but enhanced with the application of error filter cascaded to the fractional-order PI. The controller was applied on steam temperature process that was described by FOPDT transfer function. The process can be classified as lag dominating process with very small relative dead-time. The proposed control scheme was compared with other PI controller tuned using Ziegler-Nichols and AMIGO rules. Other PI controller with fractional-order integrator known as F-MIGO was also considered. All the controllers were subjected to set point change and load disturbance tests. The performance was measured using Integral of Squared Error (ISE) and Integral of Control Signal (ICO). The proposed controller produced best performance for all the tests with the least ISE index.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=PID%20controller" title="PID controller">PID controller</a>, <a href="https://publications.waset.org/search?q=fractional-order%20PID%20controller" title=" fractional-order PID controller"> fractional-order PID controller</a>, <a href="https://publications.waset.org/search?q=PI%0D%0Acontrol%20tuning" title=" PI control tuning"> PI control tuning</a>, <a href="https://publications.waset.org/search?q=steam%20temperature%20control" title=" steam temperature control"> steam temperature control</a>, <a href="https://publications.waset.org/search?q=Ziegler-Nichols%20tuning." title=" Ziegler-Nichols tuning."> Ziegler-Nichols tuning.</a> </p> <a href="https://publications.waset.org/16532/robust-fractional-order-pi-controller-with-ziegler-nichols-rules" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16532/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16532/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16532/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16532/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16532/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16532/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16532/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16532/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16532/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16532/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16532.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">3491</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">5925</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">1572</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">5924</span> Tuning a Fractional Order PID Controller with Lead Compensator in Frequency Domain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Tahmine.%20V.%20Moghaddam">Tahmine. V. Moghaddam</a>, <a href="https://publications.waset.org/search?q=N.%20Bigdeli"> N. Bigdeli</a>, <a href="https://publications.waset.org/search?q=K.%20Afshar"> K. Afshar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> To achieve the desired specifications of gain and phase margins for plants with time-delay that stabilized with FO-PID controller a lead compensator is designed. At first the range of controlled system stability based on stability boundary criteria is determined. Using stability boundary locus method in frequency domain the fractional order controller parameters are tuned and then with drawing bode diagram in frequency domain accessing to desired gain and phase margin are shown. Numerical examples are given to illustrate the shapes of the stabilizing region and to show the design procedure. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20controller" title="Fractional controller">Fractional controller</a>, <a href="https://publications.waset.org/search?q=Lead%20compensator" title=" Lead compensator"> Lead compensator</a>, <a href="https://publications.waset.org/search?q=Stabilityregions" title=" Stabilityregions"> Stabilityregions</a>, <a href="https://publications.waset.org/search?q=Stability%20boundary%20locus" title=" Stability boundary locus"> Stability boundary locus</a> </p> <a href="https://publications.waset.org/11611/tuning-a-fractional-order-pid-controller-with-lead-compensator-in-frequency-domain" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11611/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11611/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11611/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11611/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11611/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11611/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11611/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11611/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11611/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11611/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11611.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">2600</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">5923</span> Doubly Fed Induction Generator Based Variable Speed Wind Conversion System Control Enhancement by Applying Fractional Order Controller</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Abdellatif%20Kasbi">Abdellatif Kasbi</a>, <a href="https://publications.waset.org/search?q=Abderrafii%20Rahali"> Abderrafii Rahali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In an electric power grid connected wind generation system, dynamic control strategy is essential to use the wind energy efficiently as well as for an energy optimization. The present study has focused on decoupled power regulation of doubly fed induction generator, operating in wind turbine, in accordance with the vector control approach by applying fractional order proportional integral (FOPI) controller. The FOPI controller is designed based on a simple method; up such that the response of closed loop process is similar to the response of a specified fractional model whose transfer function is Bode’s ideal function. In this tuning operation, the parameters of the proposed fractional controller are established analytically using the impulse closed-loop response of the controlled process. To show the superior action of the developed FOPI controller in comparison with standard PI controller in different function conditions, the study is validated through simulation using the software MATLAB/Simulink.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Wind%20generation%20system" title="Wind generation system">Wind generation system</a>, <a href="https://publications.waset.org/search?q=DFIG" title=" DFIG"> DFIG</a>, <a href="https://publications.waset.org/search?q=vector%20control%20approach" title=" vector control approach"> vector control approach</a>, <a href="https://publications.waset.org/search?q=fractional%20order%20PI%20controller" title=" fractional order PI controller"> fractional order PI controller</a>, <a href="https://publications.waset.org/search?q=Bode%E2%80%99s%20ideal%20transfer%20function" title=" Bode’s ideal transfer function"> Bode’s ideal transfer function</a>, <a href="https://publications.waset.org/search?q=impulse%20response." title=" impulse response."> impulse response.</a> </p> <a href="https://publications.waset.org/10010884/doubly-fed-induction-generator-based-variable-speed-wind-conversion-system-control-enhancement-by-applying-fractional-order-controller" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010884/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010884/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010884/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010884/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010884/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010884/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010884/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010884/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010884/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010884/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010884.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">691</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">5922</span> Fractional Order Controller Design for Vibration Attenuation in an Airplane Wing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Birs%20Isabela">Birs Isabela</a>, <a href="https://publications.waset.org/search?q=Muresan%20Cristina"> Muresan Cristina</a>, <a href="https://publications.waset.org/search?q=Folea%20Silviu"> Folea Silviu</a>, <a href="https://publications.waset.org/search?q=Prodan%20Ovidiu"> Prodan Ovidiu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p class="Abstract" style="text-indent:10.2pt;line-height:normal"><span lang="EN-US">The wing is one of the most important parts of an airplane because it ensures stability, sustenance and maneuverability of the airplane. Because of its shape, the airplane wing can be simplified to a smart beam. Active vibration suppression is realized using piezoelectric actuators that are mounted on the surface of the beam. This work presents a tuning procedure of fractional order controllers based on a graphical approach of the frequency domain representation. The efficacy of the method is proven by practically testing the controller on a laboratory scale experimental stand.<o:p></o:p></span></p> <p class="card-text"><strong>Keywords:</strong> <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=piezoelectric%20actuators" title=" piezoelectric actuators"> piezoelectric actuators</a>, <a href="https://publications.waset.org/search?q=smart%20beam" title=" smart beam"> smart beam</a>, <a href="https://publications.waset.org/search?q=vibration%20suppression." title=" vibration suppression. "> vibration suppression. </a> </p> <a href="https://publications.waset.org/10005617/fractional-order-controller-design-for-vibration-attenuation-in-an-airplane-wing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10005617/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10005617/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10005617/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10005617/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10005617/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10005617/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10005617/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10005617/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10005617/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10005617/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10005617.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">1253</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">5921</span> Design a Fractional Order Controller for Power Control of Doubly Fed Induction Generator Based Wind Generation System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Abdellatif%20Kasbi">Abdellatif Kasbi</a>, <a href="https://publications.waset.org/search?q=Abderrafii%20Rahali"> Abderrafii Rahali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>During the recent years, much interest has been devoted to fractional order control that has appeared as a very eligible control approach for the systems experiencing parametric uncertainty and outer disturbances. The main purpose of this paper is to design and evaluate the performance of a fractional order proportional integral (FOPI) controller applied to control prototype variable speed wind generation system (WGS) that uses a doubly fed induction generator (DFIG). In this paper, the DFIG-machine is controlled according to the stator field-oriented control (FOC) strategy, which makes it possible to regulate separately the reactive and active powers exchanged between the WGS and the grid. The considered system is modeled and simulated using MATLAB-Simulink, and the performance of FOPI controller applied to the back-to-back power converter control of DFIG based grid connected variable speed wind turbine are evaluated and compared to the ones obtained with a conventional PI controller.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Design" title="Design">Design</a>, <a href="https://publications.waset.org/search?q=fractional%20order%20PI%20controller" title=" fractional order PI controller"> fractional order PI controller</a>, <a href="https://publications.waset.org/search?q=wind%20generation%20system" title=" wind generation system"> wind generation system</a>, <a href="https://publications.waset.org/search?q=doubly%20fed%20induction%20generator" title=" doubly fed induction generator"> doubly fed induction generator</a>, <a href="https://publications.waset.org/search?q=wind%20turbine" title=" wind turbine"> wind turbine</a>, <a href="https://publications.waset.org/search?q=field-oriented%20control." title=" field-oriented control."> field-oriented control.</a> </p> <a href="https://publications.waset.org/10010674/design-a-fractional-order-controller-for-power-control-of-doubly-fed-induction-generator-based-wind-generation-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010674/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010674/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010674/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010674/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010674/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010674/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010674/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010674/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010674/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010674/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010674.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">752</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">5920</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">1251</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">5919</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">3631</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">5918</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">3183</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">5917</span> Stability Analysis of Fractional Order Systems with Time Delay</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, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.</p> <p class="card-text"><strong>Keywords:</strong> <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=Time%20delay" title=" Time delay"> Time delay</a>, <a href="https://publications.waset.org/search?q=Characteristic%20equation." title=" Characteristic equation."> Characteristic equation.</a> </p> <a href="https://publications.waset.org/9998059/stability-analysis-of-fractional-order-systems-with-time-delay" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9998059/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9998059/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9998059/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9998059/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9998059/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9998059/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9998059/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9998059/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9998059/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9998059/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9998059.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">3683</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">5916</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">1217</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">5915</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">1085</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">5914</span> Backstepping Sliding Mode Controller Coupled to Adaptive Sliding Mode Observer for Interconnected Fractional Nonlinear System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=D.%20Elleuch">D. Elleuch</a>, <a href="https://publications.waset.org/search?q=T.%20Damak"> T. Damak</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Performance control law is studied for an interconnected fractional nonlinear system. Applying a backstepping algorithm, a backstepping sliding mode controller (BSMC) is developed for fractional nonlinear system. To improve control law performance, BSMC is coupled to an adaptive sliding mode observer have a filtered error as a sliding surface. The both architecture performance is studied throughout the inverted pendulum mounted on a cart. Simulation result show that the BSMC coupled to an adaptive sliding mode observer have stable control law and eligible control amplitude than the BSMC. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Backstepping%20sliding%20mode%20controller" title="Backstepping sliding mode controller">Backstepping sliding mode controller</a>, <a href="https://publications.waset.org/search?q=interconnected%20fractional%20nonlinear%20system" title=" interconnected fractional nonlinear system"> interconnected fractional nonlinear system</a>, <a href="https://publications.waset.org/search?q=adaptive%20sliding%20mode%0Aobserver." title=" adaptive sliding mode observer."> adaptive sliding mode observer.</a> </p> <a href="https://publications.waset.org/2358/backstepping-sliding-mode-controller-coupled-to-adaptive-sliding-mode-observer-for-interconnected-fractional-nonlinear-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2358/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2358/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2358/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2358/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2358/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2358/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2358/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2358/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2358/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2358/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2358.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">2306</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">5913</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">1486</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">5912</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">902</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">5911</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">1548</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">5910</span> Finite-time Stability Analysis of Fractional-order with Multi-state Time Delay</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Liqiong%20Liu">Liqiong Liu</a>, <a href="https://publications.waset.org/search?q=Shouming%20Zhong"> Shouming Zhong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Finite-time%20stabilization" title="Finite-time stabilization">Finite-time stabilization</a>, <a href="https://publications.waset.org/search?q=fractional-order%20system" title=" fractional-order system"> fractional-order system</a>, <a href="https://publications.waset.org/search?q=Gronwall%20inequality." title=" Gronwall inequality."> Gronwall inequality.</a> </p> <a href="https://publications.waset.org/3656/finite-time-stability-analysis-of-fractional-order-with-multi-state-time-delay" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3656/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3656/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3656/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3656/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3656/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3656/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3656/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3656/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3656/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3656/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3656.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">1915</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">5909</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">1217</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">5908</span> Measurement Fractional Order Sallen-Key Filters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmed%20Soltan">Ahmed Soltan</a>, <a href="https://publications.waset.org/search?q=Ahmed%20G.%20Radwan"> Ahmed G. Radwan</a>, <a href="https://publications.waset.org/search?q=Ahmed%20M.%20Soliman"> Ahmed M. Soliman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Analog%20Filter" title="Analog Filter">Analog Filter</a>, <a href="https://publications.waset.org/search?q=Low-Pass%20Filter" title=" Low-Pass Filter"> Low-Pass Filter</a>, <a href="https://publications.waset.org/search?q=Fractance" title=" Fractance"> Fractance</a>, <a href="https://publications.waset.org/search?q=Sallen-Key" title=" Sallen-Key"> Sallen-Key</a>, <a href="https://publications.waset.org/search?q=Stability." title=" Stability."> Stability.</a> </p> <a href="https://publications.waset.org/9996585/measurement-fractional-order-sallen-key-filters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9996585/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9996585/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9996585/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9996585/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9996585/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9996585/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9996585/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9996585/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9996585/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9996585/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9996585.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">3158</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">5907</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 href="https://publications.waset.org/9485/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9485/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9485/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9485/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9485/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9485/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9485/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9485/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9485/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9485/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9485.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">5906</span> Synthesis of Digital Circuits with Genetic Algorithms: A Fractional-Order Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Cec%C3%ADlia%20Reis">Cecília Reis</a>, <a href="https://publications.waset.org/search?q=J.%20A.%20Tenreiro%20Machado"> J. A. Tenreiro Machado</a>, <a href="https://publications.waset.org/search?q=J.%20Boaventura%20Cunha"> J. Boaventura Cunha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Circuit%20design" title="Circuit design">Circuit design</a>, <a href="https://publications.waset.org/search?q=fractional-order%20systems" title=" fractional-order systems"> fractional-order systems</a>, <a href="https://publications.waset.org/search?q=genetic%20algorithms" title=" genetic algorithms"> genetic algorithms</a>, <a href="https://publications.waset.org/search?q=logic%20circuits." title=" logic circuits."> logic circuits.</a> </p> <a href="https://publications.waset.org/12416/synthesis-of-digital-circuits-with-genetic-algorithms-a-fractional-order-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12416/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12416/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12416/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12416/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12416/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12416/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12416/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12416/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12416/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12416/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12416.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">1436</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">5905</span> Backstepping Design and Fractional Derivative Equation of Chaotic System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ayub%20Khan">Ayub Khan</a>, <a href="https://publications.waset.org/search?q=Net%20Ram%20Garg"> Net Ram Garg</a>, <a href="https://publications.waset.org/search?q=Geeta%20Jain"> Geeta Jain</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Backstepping%20method" title="Backstepping method">Backstepping method</a>, <a href="https://publications.waset.org/search?q=Fractional%20order" title=" Fractional order"> Fractional order</a>, <a href="https://publications.waset.org/search?q=Synchronization." title=" Synchronization."> Synchronization.</a> </p> <a href="https://publications.waset.org/9998720/backstepping-design-and-fractional-derivative-equation-of-chaotic-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9998720/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9998720/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9998720/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9998720/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9998720/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9998720/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9998720/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9998720/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9998720/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9998720/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9998720.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">2161</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">5904</span> Synthesis of Logic Circuits Using Fractional-Order Dynamic Fitness Functions </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Cec%C3%ADlia%20Reis">Cecília Reis</a>, <a href="https://publications.waset.org/search?q=J.%20A.%20Tenreiro%20Machado"> J. A. Tenreiro Machado</a>, <a href="https://publications.waset.org/search?q=J.%20Boaventura%20Cunha"> J. Boaventura Cunha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Circuit%20design" title="Circuit design">Circuit design</a>, <a href="https://publications.waset.org/search?q=fractional-order%20systems" title=" fractional-order systems"> fractional-order systems</a>, <a href="https://publications.waset.org/search?q=genetic%20algorithms" title=" genetic algorithms"> genetic algorithms</a>, <a href="https://publications.waset.org/search?q=logic%20circuits" title=" logic circuits"> logic circuits</a> </p> <a href="https://publications.waset.org/2997/synthesis-of-logic-circuits-using-fractional-order-dynamic-fitness-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2997/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2997/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2997/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2997/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2997/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2997/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2997/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2997/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2997/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2997/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2997.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">1747</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">5903</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">586</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">5902</span> Evaluation of a PSO Approach for Optimum Design of a First-Order Controllers for TCP/AQM Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sana%20Testouri">Sana Testouri</a>, <a href="https://publications.waset.org/search?q=Karim%20Saadaoui"> Karim Saadaoui</a>, <a href="https://publications.waset.org/search?q=Mohamed%20Benrejeb"> Mohamed Benrejeb</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a Particle Swarm Optimization (PSO) method for determining the optimal parameters of a first-order controller for TCP/AQM system. The model TCP/AQM is described by a second-order system with time delay. First, the analytical approach, based on the D-decomposition method and Lemma of Kharitonov, is used to determine the stabilizing regions of a firstorder controller. Second, the optimal parameters of the controller are obtained by the PSO algorithm. Finally, the proposed method is implemented in the Network Simulator NS-2 and compared with the PI controller. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=AQM" title="AQM">AQM</a>, <a href="https://publications.waset.org/search?q=first-order%20controller" title=" first-order controller"> first-order controller</a>, <a href="https://publications.waset.org/search?q=time%20delay" title=" time delay"> time delay</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=PSO." title=" PSO."> PSO.</a> </p> <a href="https://publications.waset.org/3122/evaluation-of-a-pso-approach-for-optimum-design-of-a-first-order-controllers-for-tcpaqm-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3122/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3122/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3122/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3122/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3122/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3122/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3122/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3122/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3122/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3122/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3122.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">1780</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">5901</span> An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Haniye%20Dehestani">Haniye Dehestani</a>, <a href="https://publications.waset.org/search?q=Yadollah%20Ordokhani"> Yadollah Ordokhani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Collocation%20method" title="Collocation method">Collocation method</a>, <a href="https://publications.waset.org/search?q=fractional%20partial%20differential%0D%0Aequations" title=" fractional partial differential equations"> fractional partial differential equations</a>, <a href="https://publications.waset.org/search?q=Legendre-Laguerre%20functions" title=" Legendre-Laguerre functions"> Legendre-Laguerre functions</a>, <a href="https://publications.waset.org/search?q=pseudo-operational%20matrix%0D%0Aof%20integration." title=" pseudo-operational matrix of integration."> pseudo-operational matrix of integration.</a> </p> <a 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