Exact Solutions of the Space-Time Fractional Bidirectional Wave Equations Using the (G′/G)-Expansion Method

Abstract

Based on Jumarie’s modified Riemann-Liouville derivative, the fractional complex transformation is used to transform fractional differential equations to ordinary differential equations. Exact solutions including the hyperbolic functions, the trigonometric functions, and the rational functions for the space-time fractional bidirectional wave equations are obtained using the $(G^{\prime }/G)$-expansion method. The method provides a promising tool for solving nonlinear fractional differential equations.