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Advances in Mathematical Physics
Volume 2017, Article ID 1535826, 14 pages
Research Article

Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

1Department of Mathematics, Sun Yat-Sen University, Guangzhou, China
2Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhwa, Pakistan

Correspondence should be addressed to Kamal Shah; moc.liamg@804hahslamak

Received 26 May 2017; Revised 11 July 2017; Accepted 16 July 2017; Published 20 September 2017

Academic Editor: Rehana Naz

Copyright © 2017 Yongjin Li and Kamal Shah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique.