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fractional transformation (LFT)</title> <meta name="description" content="Search results for: linear fractional transformation (LFT)"> <meta name="keywords" content="linear fractional transformation (LFT)"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science 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method="get" action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="linear fractional transformation (LFT)"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 5110</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: linear fractional transformation (LFT)</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5110</span> Online Robust Model Predictive Control for Linear Fractional Transformation Systems Using Linear Matrix Inequalities</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Peyman%20Sindareh%20Esfahani">Peyman Sindareh Esfahani</a>, <a href="https://publications.waset.org/abstracts/search?q=Jeffery%20Kurt%20Pieper"> Jeffery Kurt Pieper</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the <em>l</em><sub>2</sub>-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20fractional%20transformation" title="linear fractional transformation">linear fractional transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequality" title=" linear matrix inequality"> linear matrix inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20model%20predictive%20control" title=" robust model predictive control"> robust model predictive control</a>, <a href="https://publications.waset.org/abstracts/search?q=state%20feedback%20control" title=" state feedback control"> state feedback control</a> </p> <a href="https://publications.waset.org/abstracts/69466/online-robust-model-predictive-control-for-linear-fractional-transformation-systems-using-linear-matrix-inequalities" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/69466.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">395</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5109</span> Interval Bilevel Linear Fractional Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20Hamidi">F. Hamidi</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Amiri"> N. Amiri</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Mishmast%20Nehi"> H. Mishmast Nehi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Bilevel Programming (BP) model has been presented for a decision making process that consists of two decision makers in a hierarchical structure. In fact, BP is a model for a static two person game (the leader player in the upper level and the follower player in the lower level) wherein each player tries to optimize his/her personal objective function under dependent constraints; this game is sequential and non-cooperative. The decision making variables are divided between the two players and one’s choice affects the other’s beneﬁt and choices. In other words, BP consists of two nested optimization problems with two objective functions (upper and lower) where the constraint region of the upper level problem is implicitly determined by the lower level problem. In real cases, the coeﬃcients of an optimization problem may not be precise, i.e. they may be interval. In this paper we develop an algorithm for solving interval bilevel linear fractional programming problems. That is to say, bilevel problems in which both objective functions are linear fractional, the coefficients are interval and the common constraint region is a polyhedron. From the original problem, the best and the worst bilevel linear fractional problems have been derived and then, using the extended Charnes and Cooper transformation, each fractional problem can be reduced to a linear problem. Then we can ﬁnd the best and the worst optimal values of the leader objective function by two algorithms. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=best%20and%20worst%20optimal%20solutions" title="best and worst optimal solutions">best and worst optimal solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=bilevel%20programming" title=" bilevel programming"> bilevel programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional" title=" fractional"> fractional</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20coefficients" title=" interval coefficients"> interval coefficients</a> </p> <a href="https://publications.waset.org/abstracts/34778/interval-bilevel-linear-fractional-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34778.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">446</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5108</span> Commutativity of Fractional Order Linear Time-Varying Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Salisu%20Ibrahim">Salisu Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20differential%20equation" title="fractional differential equation">fractional differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=physical%20systems" title=" physical systems"> physical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalent%20circuit" title=" equivalent circuit"> equivalent circuit</a>, <a href="https://publications.waset.org/abstracts/search?q=analog%20control" title=" analog control"> analog control</a> </p> <a href="https://publications.waset.org/abstracts/171951/commutativity-of-fractional-order-linear-time-varying-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171951.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">114</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5107</span> Commutativity of Fractional Order Linear Time-Varying System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Salisu%20Ibrahim">Salisu Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20differential%20equation" title="fractional differential equation">fractional differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=physical%20systems" title=" physical systems"> physical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalent%20circuit" title=" equivalent circuit"> equivalent circuit</a>, <a href="https://publications.waset.org/abstracts/search?q=and%20analog%20control" title=" and analog control"> and analog control</a> </p> <a href="https://publications.waset.org/abstracts/172277/commutativity-of-fractional-order-linear-time-varying-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/172277.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">77</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5106</span> Approximations of Fractional Derivatives and Its Applications in Solving Non-Linear Fractional Variational Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Harendra%20Singh">Harendra Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajesh%20Pandey"> Rajesh Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20fractional%20variational%20problems" title="non-linear fractional variational problems">non-linear fractional variational problems</a>, <a href="https://publications.waset.org/abstracts/search?q=Rayleigh-Ritz%20method" title=" Rayleigh-Ritz method"> Rayleigh-Ritz method</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20analysis" title=" convergence analysis"> convergence analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20analysis" title=" error analysis"> error analysis</a> </p> <a href="https://publications.waset.org/abstracts/57497/approximations-of-fractional-derivatives-and-its-applications-in-solving-non-linear-fractional-variational-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57497.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">298</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5105</span> Linear fractional differential equations for second kind modified Bessel functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares">Jorge Olivares</a>, <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass"> Fernando Maass</a>, <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin"> Pablo Martin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo" title="Caputo">Caputo</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20Bessel%20functions" title=" modified Bessel functions"> modified Bessel functions</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergeometric" title=" hypergeometric"> hypergeometric</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20fractional%20differential%20equations" title=" linear fractional differential equations"> linear fractional differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=transform%20Laplace" title=" transform Laplace"> transform Laplace</a> </p> <a href="https://publications.waset.org/abstracts/91374/linear-fractional-differential-equations-for-second-kind-modified-bessel-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91374.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">342</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5104</span> Robust Diagnosis of an Electro-Mechanical Actuators, Bond Graph LFT Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Boulanoir">A. Boulanoir</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Ould%20Bouamama"> B. Ould Bouamama</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Debiane"> A. Debiane</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Achour"> N. Achour</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper deals with robust Fault Detection and isolation with respect to parameter uncertainties based on linear fractional transformation form (LFT) Bond graph. The innovative interest of the proposed methodology is the use only one representation for systematic generation of robust analytical redundancy relations and adaptive residual thresholds for sensibility analysis. Furthermore, the parameter uncertainties are introduced graphically in the bond graph model. The methodology applied to the nonlinear industrial Electro-Mechanical Actuators (EMA) used in avionic systems, has determined first the structural monitorability analysis (which component can be monitored) with given instrumentation architecture with any need of complex calculation and secondly robust fault indicators for online supervision. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bond%20graph%20%28BG%29" title="bond graph (BG)">bond graph (BG)</a>, <a href="https://publications.waset.org/abstracts/search?q=electro%20mechanical%20actuators%20%28EMA%29" title=" electro mechanical actuators (EMA)"> electro mechanical actuators (EMA)</a>, <a href="https://publications.waset.org/abstracts/search?q=fault%20detection%20and%20isolation%20%28FDI%29" title=" fault detection and isolation (FDI)"> fault detection and isolation (FDI)</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20fractional%20transformation%20%28LFT%29" title=" linear fractional transformation (LFT)"> linear fractional transformation (LFT)</a>, <a href="https://publications.waset.org/abstracts/search?q=mechatronic%20systems" title=" mechatronic systems"> mechatronic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=parameter%20uncertainties" title=" parameter uncertainties"> parameter uncertainties</a>, <a href="https://publications.waset.org/abstracts/search?q=avionic%20system" title=" avionic system"> avionic system</a> </p> <a href="https://publications.waset.org/abstracts/29219/robust-diagnosis-of-an-electro-mechanical-actuators-bond-graph-lft-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29219.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">350</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5103</span> A Fuzzy Programming Approach for Solving Intuitionistic Fuzzy Linear Fractional Programming Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sujeet%20Kumar%20Singh">Sujeet Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Shiv%20Prasad%20Yadav"> Shiv Prasad Yadav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=triangular%20intuitionistic%20fuzzy%20number" title="triangular intuitionistic fuzzy number">triangular intuitionistic fuzzy number</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming%20problem" title=" linear programming problem"> linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20objective%20linear%20programming%20problem" title=" multi objective linear programming problem"> multi objective linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20mathematical%20programming" title=" fuzzy mathematical programming"> fuzzy mathematical programming</a>, <a href="https://publications.waset.org/abstracts/search?q=membership%20function" title=" membership function"> membership function</a> </p> <a href="https://publications.waset.org/abstracts/16411/a-fuzzy-programming-approach-for-solving-intuitionistic-fuzzy-linear-fractional-programming-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16411.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">566</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5102</span> Mixed Sub-Fractional Brownian Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mounir%20Zili">Mounir Zili</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-Markovian and that it has non-stationary increments. We will also give the conditions under which it is a semimartingale. Finally, the main features of its sample paths will be specified. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mixed%20Gaussian%20processes" title="mixed Gaussian processes">mixed Gaussian processes</a>, <a href="https://publications.waset.org/abstracts/search?q=Sub-fractional%20Brownian%20motion" title=" Sub-fractional Brownian motion"> Sub-fractional Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=sample%20paths" title=" sample paths"> sample paths</a> </p> <a href="https://publications.waset.org/abstracts/32479/mixed-sub-fractional-brownian-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32479.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">488</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5101</span> Mixed-Sub Fractional Brownian Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mounir%20Zili">Mounir Zili</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-markovian and that it has non-stationary increments. We will also give the conditions under which it is a semi-martingale. Finally, the main features of its sample paths will be specified. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractal%20dimensions" title="fractal dimensions">fractal dimensions</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20gaussian%20processes" title=" mixed gaussian processes"> mixed gaussian processes</a>, <a href="https://publications.waset.org/abstracts/search?q=sample%20paths" title=" sample paths"> sample paths</a>, <a href="https://publications.waset.org/abstracts/search?q=sub-fractional%20brownian%20motion" title=" sub-fractional brownian motion "> sub-fractional brownian motion </a> </p> <a href="https://publications.waset.org/abstracts/36677/mixed-sub-fractional-brownian-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36677.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">420</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5100</span> Modified Fractional Curl Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rawhy%20Ismail">Rawhy Ismail </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=curl%20operator" title="curl operator">curl operator</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20curl%20operators" title=" fractional curl operators"> fractional curl operators</a>, <a href="https://publications.waset.org/abstracts/search?q=Maxwell%20equations" title=" Maxwell equations"> Maxwell equations</a> </p> <a href="https://publications.waset.org/abstracts/35772/modified-fractional-curl-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35772.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">487</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5099</span> Hypergeometric Solutions to Linear Nonhomogeneous Fractional Equations with Spherical Bessel Functions of the First Kind</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin">Pablo Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares"> Jorge Olivares</a>, <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass"> Fernando Maass</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=caputo%20fractional%20derivatives" title="caputo fractional derivatives">caputo fractional derivatives</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergeometric%20functions" title=" hypergeometric functions"> hypergeometric functions</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20differential%20equations" title=" linear differential equations"> linear differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=spherical%20Bessel%20functions" title=" spherical Bessel functions"> spherical Bessel functions</a> </p> <a href="https://publications.waset.org/abstracts/91343/hypergeometric-solutions-to-linear-nonhomogeneous-fractional-equations-with-spherical-bessel-functions-of-the-first-kind" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91343.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">325</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5098</span> Numerical Solution of Space Fractional Order Linear/Nonlinear Reaction-Advection Diffusion Equation Using Jacobi Polynomial</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=space%20fractional%20order%20linear%2Fnonlinear%20reaction-advection%20diffusion%20equation" title="space fractional order linear/nonlinear reaction-advection diffusion equation">space fractional order linear/nonlinear reaction-advection diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=shifted%20Jacobi%20polynomials" title=" shifted Jacobi polynomials"> shifted Jacobi polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrix" title=" operational matrix"> operational matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title=" collocation method"> collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20derivative" title=" Caputo derivative"> Caputo derivative</a> </p> <a href="https://publications.waset.org/abstracts/79521/numerical-solution-of-space-fractional-order-linearnonlinear-reaction-advection-diffusion-equation-using-jacobi-polynomial" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79521.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">445</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5097</span> Magnetohydrodynamic Couette Flow of Fractional Burger’s Fluid in an Annulus</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sani%20Isa">Sani Isa</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20Musa"> Ali Musa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Burgers’ fluid with a fractional derivatives model in an annulus was analyzed. Combining appropriately the basic equations, with the fractionalized fractional Burger’s fluid model allow us to determine the velocity field, temperature and shear stress. The governing partial differential equation was solved using the combine Laplace transformation method and Riemann sum approximation to give velocity field, temperature and shear stress on the fluid flow. The influence of various parameters like fractional parameters, relaxation time and retardation time, are drawn. The results obtained are simulated using Mathcad software and presented graphically. From the graphical results, we observed that the relaxation time and time helps the flow pattern, on the other hand, other material constants resist the fluid flow while fractional parameters effect on fluid flow is opposite to each other. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=sani%20isa" title="sani isa">sani isa</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20musaburger%E2%80%99s%20fluid" title=" Ali musaburger’s fluid"> Ali musaburger’s fluid</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplace%20transform" title=" Laplace transform"> Laplace transform</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivatives" title=" fractional derivatives"> fractional derivatives</a>, <a href="https://publications.waset.org/abstracts/search?q=annulus" title=" annulus"> annulus</a> </p> <a href="https://publications.waset.org/abstracts/190150/magnetohydrodynamic-couette-flow-of-fractional-burgers-fluid-in-an-annulus" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/190150.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">24</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5096</span> Fractional Calculus into Structural Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Lopez">Jorge Lopez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we introduce fractional calculus in order to study the dynamics of a damped multistory building with some symmetry. Initially we make a review of the dynamics of a free and damped multistory building. Then we introduce those concepts of fractional calculus that will be involved in our study. It has been noticed that fractional calculus provides models with less parameters than those based on classical calculus. In particular, a damped classical oscilator is more naturally described by using fractional derivatives. Accordingly, we model our multistory building as a set of coupled fractional oscillators and compare its dynamics with the results coming from traditional methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coupled%20oscillators" title="coupled oscillators">coupled oscillators</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20oscillator" title=" fractional oscillator"> fractional oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20dynamics" title=" structural dynamics"> structural dynamics</a> </p> <a href="https://publications.waset.org/abstracts/124822/fractional-calculus-into-structural-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124822.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">242</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5095</span> Nonhomogeneous Linear Fractional Differential Equations Will Bessel Functions of the First Kind Giving Hypergeometric Functions Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass">Fernando Maass</a>, <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin"> Pablo Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares"> Jorge Olivares</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo" title="Caputo">Caputo</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculation" title=" fractional calculation"> fractional calculation</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergeometric" title=" hypergeometric"> hypergeometric</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20differential%20equations" title=" linear differential equations"> linear differential equations</a> </p> <a href="https://publications.waset.org/abstracts/91373/nonhomogeneous-linear-fractional-differential-equations-will-bessel-functions-of-the-first-kind-giving-hypergeometric-functions-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91373.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">197</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5094</span> Fractional Order Differentiator Using Chebyshev Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Koushlendra%20Kumar%20Singh">Koushlendra Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Manish%20Kumar%20Bajpai"> Manish Kumar Bajpai</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajesh%20Kumar%20Pandey"> Rajesh Kumar Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A discrete time fractional orderdifferentiator has been modeled for estimating the fractional order derivatives of contaminated signal. The proposed approach is based on Chebyshev’s polynomials. We use the Riemann-Liouville fractional order derivative definition for designing the fractional order SG differentiator. In first step we calculate the window weight corresponding to the required fractional order. Then signal is convoluted with this calculated window’s weight for finding the fractional order derivatives of signals. Several signals are considered for evaluating the accuracy of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20derivative" title="fractional order derivative">fractional order derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=chebyshev%0D%0Apolynomials" title=" chebyshev polynomials"> chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=signals" title=" signals"> signals</a>, <a href="https://publications.waset.org/abstracts/search?q=S-G%20differentiator" title=" S-G differentiator"> S-G differentiator</a> </p> <a href="https://publications.waset.org/abstracts/21346/fractional-order-differentiator-using-chebyshev-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21346.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">648</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5093</span> An Algorithm to Find Fractional Edge Domination Number and Upper Fractional Edge Domination Number of an Intuitionistic Fuzzy Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Karunambigai%20Mevani%20Govindasamy">Karunambigai Mevani Govindasamy</a>, <a href="https://publications.waset.org/abstracts/search?q=Sathishkumar%20Ayyappan"> Sathishkumar Ayyappan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we formulate the algorithm to find out the dominating function parameters of Intuitionistic Fuzzy Graphs(IFG). The methodology we adopted here is converting any physical problem into an IFG, and that has been transformed into Intuitionistic Fuzzy Matrix. Using Linear Program Solver software (LiPS), we found the defined parameters for the given IFG. We obtained these parameters for a path and cycle IFG. This study can be extended to other varieties of IFG. In particular, we obtain the definition of edge dominating function, minimal edge dominating function, fractional edge domination number (γ_if^') and upper fractional edge domination number (Γ_if^') of an intuitionistic fuzzy graph. Also, we formulated an algorithm which is appropriate to work on LiPS to find fractional edge domination number and upper fractional edge domination number of an IFG. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20edge%20domination%20number" title="fractional edge domination number">fractional edge domination number</a>, <a href="https://publications.waset.org/abstracts/search?q=intuitionistic%20fuzzy%20cycle" title=" intuitionistic fuzzy cycle"> intuitionistic fuzzy cycle</a>, <a href="https://publications.waset.org/abstracts/search?q=intuitionistic%20fuzzy%20graph" title=" intuitionistic fuzzy graph"> intuitionistic fuzzy graph</a>, <a href="https://publications.waset.org/abstracts/search?q=intuitionistic%20fuzzy%20path" title=" intuitionistic fuzzy path"> intuitionistic fuzzy path</a> </p> <a href="https://publications.waset.org/abstracts/112004/an-algorithm-to-find-fractional-edge-domination-number-and-upper-fractional-edge-domination-number-of-an-intuitionistic-fuzzy-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/112004.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">174</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5092</span> Observer-Based Leader-Following Consensus of Nonlinear Fractional-Order Multi-Agent Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Afaghi">Ali Afaghi</a>, <a href="https://publications.waset.org/abstracts/search?q=Sehraneh%20Ghaemi"> Sehraneh Ghaemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional-order%20multi-agent%20systems" title="fractional-order multi-agent systems">fractional-order multi-agent systems</a>, <a href="https://publications.waset.org/abstracts/search?q=leader-following%20consensus" title=" leader-following consensus"> leader-following consensus</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20dynamics" title=" nonlinear dynamics"> nonlinear dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=directed%20graphs" title=" directed graphs"> directed graphs</a> </p> <a href="https://publications.waset.org/abstracts/67272/observer-based-leader-following-consensus-of-nonlinear-fractional-order-multi-agent-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67272.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">398</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5091</span> Fractional Euler Method and Finite Difference Formula Using Conformable Fractional Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramzi%20B.%20Albadarneh">Ramzi B. Albadarneh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conformable%20fractional%20derivative" title="conformable fractional derivative">conformable fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivative" title=" fractional derivative"> fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a> </p> <a href="https://publications.waset.org/abstracts/37072/fractional-euler-method-and-finite-difference-formula-using-conformable-fractional-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37072.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">439</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5090</span> Numerical Solution of Magneto-Hydrodynamic Flow of a Viscous Fluid in the Presence of Nanoparticles with Fractional Derivatives through a Cylindrical Tube</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Abdullah">Muhammad Abdullah</a>, <a href="https://publications.waset.org/abstracts/search?q=Asma%20Rashid%20Butt"> Asma Rashid Butt</a>, <a href="https://publications.waset.org/abstracts/search?q=Nauman%20Raza"> Nauman Raza</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Biomagnetic fluids like blood play key role in different applications of medical science and bioengineering. In this paper, the magnetohydrodynamic flow of a viscous fluid with magnetic particles through a cylindrical tube is investigated. The fluid is electrically charged in the presence of a uniform external magnetic field. The movement in the fluid is produced due to the cylindrical tube. Initially, the fluid and tube are at rest and at time t=0⁺, the tube starts to move along its axis. To obtain the mathematical model of flow with fractional derivatives fractional calculus approach is used. The solution of the flow model is obtained by using Laplace transformation. The Simon's numerical algorithm is employed to obtain inverse Laplace transform. The hybrid technique, we are employing has less computational effort as compared to other methods. The numerical calculations have been performed with Mathcad software. As the special cases of our problem, the solution of flow model with ordinary derivatives and flow without magnetic particles has been procured. Finally, the impact of non-integer fractional parameter alpha, Hartmann number Ha, and Reynolds number Re on flow and magnetic particles velocity is analyzed and depicted by graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=viscous%20fluid" title="viscous fluid">viscous fluid</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetic%20particles" title=" magnetic particles"> magnetic particles</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculus" title=" fractional calculus"> fractional calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=laplace%20transformation" title=" laplace transformation"> laplace transformation</a> </p> <a href="https://publications.waset.org/abstracts/90032/numerical-solution-of-magneto-hydrodynamic-flow-of-a-viscous-fluid-in-the-presence-of-nanoparticles-with-fractional-derivatives-through-a-cylindrical-tube" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/90032.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">206</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5089</span> Fundamental Solutions for Discrete Dynamical Systems Involving the Fractional Laplacian</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Gonzalez%20Camus">Jorge Gonzalez Camus</a>, <a href="https://publications.waset.org/abstracts/search?q=Valentin%20Keyantuo"> Valentin Keyantuo</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahamadi%20Warma"> Mahamadi Warma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20fractional%20Laplacian" title="discrete fractional Laplacian">discrete fractional Laplacian</a>, <a href="https://publications.waset.org/abstracts/search?q=explicit%20representation%20of%20solutions" title=" explicit representation of solutions"> explicit representation of solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20heat%20and%20wave%20equations" title=" fractional heat and wave equations"> fractional heat and wave equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fundamental" title=" fundamental"> fundamental</a> </p> <a href="https://publications.waset.org/abstracts/99922/fundamental-solutions-for-discrete-dynamical-systems-involving-the-fractional-laplacian" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99922.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">209</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5088</span> Caputo-Type Fuzzy Fractional Riccati Differential Equations with Fuzzy Initial Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Trilok%20Mathur">Trilok Mathur</a>, <a href="https://publications.waset.org/abstracts/search?q=Shivi%20Agarwal"> Shivi Agarwal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo-type%20fuzzy%20fractional%20derivative" title="Caputo-type fuzzy fractional derivative">Caputo-type fuzzy fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=Fractional%20Riccati%20differential%20equations" title=" Fractional Riccati differential equations"> Fractional Riccati differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplace-Adomian-Pade%20method" title=" Laplace-Adomian-Pade method"> Laplace-Adomian-Pade method</a>, <a href="https://publications.waset.org/abstracts/search?q=Mittag%20Leffler%20function" title=" Mittag Leffler function"> Mittag Leffler function</a> </p> <a href="https://publications.waset.org/abstracts/51080/caputo-type-fuzzy-fractional-riccati-differential-equations-with-fuzzy-initial-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51080.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">395</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5087</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/abstracts/search?q=Changhong%20Guo">Changhong Guo</a>, <a href="https://publications.waset.org/abstracts/search?q=Shaomei%20Fang"> Shaomei Fang</a>, <a href="https://publications.waset.org/abstracts/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/abstracts/search?q=European%20option%20pricing" title="European option pricing">European option pricing</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20Black-Scholes%20equations" title=" fractional Black-Scholes equations"> fractional Black-Scholes equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20g-Brownian%20motion" title=" fractional g-Brownian motion"> fractional g-Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%27s%20series%20of%20fractional%20order" title=" Taylor's series of fractional order"> Taylor's series of fractional order</a>, <a href="https://publications.waset.org/abstracts/search?q=uncertain%20volatility" title=" uncertain volatility"> uncertain volatility</a> </p> <a href="https://publications.waset.org/abstracts/127107/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/abstracts/127107.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">163</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5086</span> Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yildiray%20Keskin">Yildiray Keskin</a>, <a href="https://publications.waset.org/abstracts/search?q=Omer%20Acan"> Omer Acan</a>, <a href="https://publications.waset.org/abstracts/search?q=Murat%20Akkus"> Murat Akkus</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20diffusion%20equations" title="fractional diffusion equations">fractional diffusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20fractional%20derivative" title=" Caputo fractional derivative"> Caputo fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=reduced%20differential%20transform%20method" title=" reduced differential transform method"> reduced differential transform method</a>, <a href="https://publications.waset.org/abstracts/search?q=partial" title=" partial"> partial</a> </p> <a href="https://publications.waset.org/abstracts/17526/reduced-differential-transform-methods-for-solving-the-fractional-diffusion-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17526.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">525</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5085</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/abstracts/search?q=Ali%20Dorostkar">Ali Dorostkar</a> </p> <p class="card-text"><strong>Abstract:</strong></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 class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=tangent%20line" title="tangent line">tangent line</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20dimension" title=" fractional dimension"> fractional dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=root" title=" root"> root</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization%20problem" title=" optimization problem"> optimization problem</a> </p> <a href="https://publications.waset.org/abstracts/94257/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/abstracts/94257.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">192</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5084</span> Targeting Mineral Resources of the Upper Benue trough, Northeastern Nigeria Using Linear Spectral Unmixing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bello%20Yusuf%20Idi">Bello Yusuf Idi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Gongola arm of the Upper Banue Trough, Northeastern Nigeria is predominantly covered by the outcrops of Limestone-bearing rocks in form of Sandstone with intercalation of carbonate clay, shale, basaltic, felsphatic and migmatide rocks at subpixel dimension. In this work, subpixel classification algorithm was used to classify the data acquired from landsat 7 Enhance Thematic Mapper (ETM+) satellite system with the aim of producing fractional distribution image for three most economically important solid minerals of the area: Limestone, Basalt and Migmatide. Linear Spectral Unmixing (LSU) algorithm was used to produce fractional distribution image of abundance of the three mineral resources within a 100Km2 portion of the area. The results show that the minerals occur at different proportion all over the area. The fractional map could therefore serve as a guide to the ongoing reconnaissance for the economic potentiality of the formation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20spectral%20un-mixing" title="linear spectral un-mixing">linear spectral un-mixing</a>, <a href="https://publications.waset.org/abstracts/search?q=upper%20benue%20trough" title=" upper benue trough"> upper benue trough</a>, <a href="https://publications.waset.org/abstracts/search?q=gongola%20arm" title=" gongola arm"> gongola arm</a>, <a href="https://publications.waset.org/abstracts/search?q=geological%20engineering" title=" geological engineering"> geological engineering</a> </p> <a href="https://publications.waset.org/abstracts/7056/targeting-mineral-resources-of-the-upper-benue-trough-northeastern-nigeria-using-linear-spectral-unmixing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7056.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">373</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5083</span> Design Fractional-Order Terminal Sliding Mode Control for Synchronization of a Class of Fractional-Order Chaotic Systems with Uncertainty and External Disturbances</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shabnam%20Pashaei">Shabnam Pashaei</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammadali%20Badamchizadeh"> Mohammadali Badamchizadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a new fractional-order terminal sliding mode control for synchronization of two different fractional-order chaotic systems with uncertainty and external disturbances. A fractional-order integral type nonlinear switching surface is presented. Then, using the Lyapunov stability theory and sliding mode theory, a fractional-order control law is designed to synchronize two different fractional-order chaotic systems. Finally, a simulation example is presented to illustrate the performance and applicability of the proposed method. Based on numerical results, the proposed controller ensures that the states of the controlled fractional-order chaotic response system are asymptotically synchronized with the states of the drive system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=terminal%20sliding%20mode%20control" title="terminal sliding mode control">terminal sliding mode control</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional-order%20calculus" title=" fractional-order calculus"> fractional-order calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=chaotic%20systems" title=" chaotic systems"> chaotic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=synchronization" title=" synchronization"> synchronization</a> </p> <a href="https://publications.waset.org/abstracts/67276/design-fractional-order-terminal-sliding-mode-control-for-synchronization-of-a-class-of-fractional-order-chaotic-systems-with-uncertainty-and-external-disturbances" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67276.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">410</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5082</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/abstracts/search?q=Kazem%20Ghanbari">Kazem Ghanbari</a>, <a href="https://publications.waset.org/abstracts/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/abstracts/search?q=fractional%20derivatives%20and%20integrals" title="fractional derivatives and integrals">fractional derivatives and integrals</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamiltonian%20system" title=" Hamiltonian system"> Hamiltonian system</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov-type%20inequalities" title=" Lyapunov-type inequalities"> Lyapunov-type inequalities</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=disconjugacy" title=" disconjugacy"> disconjugacy</a> </p> <a href="https://publications.waset.org/abstracts/48806/lyapunov-type-inequalities-for-fractional-impulsive-hamiltonian-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48806.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">354</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5081</span> Solutions of Fractional Reaction-Diffusion Equations Used to Model the Growth and Spreading of Biological Species</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Al-Khaled">Kamel Al-Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some ﬁelds such as cell biology, chemistry, physics, and ﬁnance, makes it necessary to apply the results reported here to some numerical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20partial%20differential%20equations" title="fractional partial differential equations">fractional partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=reaction-di%EF%AC%80usion%20equations" title=" reaction-diﬀusion equations"> reaction-diﬀusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=adomian%20decomposition" title=" adomian decomposition"> adomian decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=biological%20species" title=" biological species"> biological species</a> </p> <a 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