THE FRACTIONAL \((D_ξ^{α}G/G)\)-EXPANSION METHOD AND ITS APPLICATIONS FOR SOLVING FOUR NONLINEAR SPACE-TIME FRACTIONAL PDES IN MATHEMATICAL PHYSICS

Abstract

The fractional \((D_ξ^{α}G/G)\)-expansion method is applied in this article to find the exact traveling wave solutions with parameters for four nonlinear space-time fractional partial differential equations (PDEs), namely the space-time fractional Potential Kadomtsev-Petviashvili (PKP) equation, the space-time fractional symmetric regularized long wave (SRLW) equation, the space-time fractional Sharma-Tasso-Olver (STO) equation and the space-time fractional Kolmogorov-Petrovskii-Piskunov (KPP) equation.  When these parameters are taken special values, we obtain three types of solutions via the solitary, trigonometric and rational solutions.  Comparison between our recent results and the well-known results is given.  The solutions of these equations with numerical simulations are presented.