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(\(G'/G\))-expansion method for solving fractional partial differential equations in the theory of mathematical physics. (English) Zbl 1264.35273

Summary: In this paper, the (\(G'/G\))-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.

MSC:

35R11 Fractional partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
44A05 General integral transforms
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