Backlund transformation of fractional Riccati equation and its applications to the space-time FDEs

In this paper, the Backlund transformation of fractional Riccati equation is presented to establish traveling wave solutions for two nonlinear space-time fractional differential equations in the sense of modified Riemann-Liouville derivatives, namely, the space-time fractional generalized reaction duffing equation and the space-time fractional diffusion reaction equation with cubic nonlinearity. The proposed method is effective and convenient for solving nonlinear evolution equations with fractional order. Copyright (C) 2014 John Wiley & Sons, Ltd.