( G ′/ G )-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics

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.