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Homotopy series solutions to time-space fractional coupled systems. (English) Zbl 1453.65381

Summary: 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.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35C10 Series solutions to PDEs
35R11 Fractional partial differential equations
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