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A generalized scheme based on shifted Jacobi polynomials for numerical simulation of coupled systems of multi-term fractional-order partial differential equations

Part of: Miscellaneous topics - Partial differential equations Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  01 July 2017

Kamal Shah ,
Hammad Khalil  and
Rahmat Ali Khan
Kamal Shah
Affiliation:
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan email kamalshah408@gmail.com
Hammad Khalil
Affiliation:
Department of Mathematics, University of Education (Attock Campus), Punjab, Pakistan email hammad.khalil@ue.edu.pk
Rahmat Ali Khan
Affiliation:
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan email rahmat_alipk@yahoo.com

Abstract

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Due to the increasing application of fractional calculus in engineering and biomedical processes, we analyze a new method for the numerical simulation of a large class of coupled systems of fractional-order partial differential equations. In this paper, we study shifted Jacobi polynomials in the case of two variables and develop some new operational matrices of fractional-order integrations as well as fractional-order differentiations. By the use of these operational matrices, we present a new and easy method for solving a generalized class of coupled systems of fractional-order partial differential equations subject to some initial conditions. We convert the system under consideration to a system of easily solvable algebraic equation without discretizing the system, and obtain a highly accurate solution. Also, the proposed method is compared with some other well-known differential transform methods. The proposed method is computer oriented. We use MatLab to perform the necessary calculation. The next two parts will appear soon.

MSC classification

Primary: 35R11: Fractional partial differential equations
Secondary: 65M06: Finite difference methods
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 20 , Issue 1 , 2017 , pp. 11 - 29
Copyright
© The Author(s) 2017 

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