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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 3540364, 19 pages
https://doi.org/10.1155/2017/3540364
Research Article

Homotopy Series Solutions to Time-Space Fractional Coupled Systems

1School of Mathematics, Jilin University, Changchun 130012, China
2School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, Jilin 130024, China

Correspondence should be addressed to Jin Zhang; nc.ude.ulj@gnahznij

Received 31 August 2017; Accepted 23 October 2017; Published 25 December 2017

Academic Editor: Jorge E. Macías-Díaz

Copyright © 2017 Jin Zhang et al. 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.

Abstract

We apply the homotopy perturbation Sumudu transform method (HPSTM) to the time-space fractional coupled systems in the sense of Riemann-Liouville fractional integral and Caputo derivative. The HPSTM is a combination of Sumudu transform and homotopy perturbation method, which can be easily handled with nonlinear coupled system. We apply the method to the coupled Burgers system, the coupled KdV system, the generalized Hirota-Satsuma coupled KdV system, the coupled WBK system, and the coupled shallow water system. The simplicity and validity of the method can be shown by the applications and the numerical results.