Abstract
In this paper, we propose a new fractional sub-equation method for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative, which is the fractional version of the known (G′/G) method. To illustrate the validity of this method, we apply it to the space-time fractional Fokas equation, the space-time fractional -dimensional dispersive long wave equations and the space-time fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established. MSC:35Q51, 35Q53.
Highlights
Fractional differential equations are generalizations of classical differential equations of integer order
We propose a new fractional sub-equation method to establish exact solutions for fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative defined by Jumarie [ ], which is a fractional version of the known (G /G) method [ – ]
3 Description of the fractional sub-equation method we describe the main steps of the fractional sub-equation method for finding exact solutions of FPDEs
Summary
Fractional differential equations are generalizations of classical differential equations of integer order. In [ ], Baleanu et al studied the existence and uniqueness of the solution for a nonlinear fractional differential equation boundary-value problem by using fixedpoint methods. Many powerful and efficient methods have been proposed to obtain numerical solutions and exact solutions of fractional differential equations so far.
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