Exact solutions of some systems of fractional differential-difference equations

In this paper, the (G'/G)-expansion method is proposed to establish hyperbolic and trigonometric function solutions for fractional differential-difference equations with themodified Riemann-Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential-difference equation into its differential-difference equation of integer order. We obtain the hyperbolic and periodic function solutions of the nonlinear time-fractional Toda lattice equations and relativistic Toda lattice system. The proposed method is more effective and powerful for obtaining exact solutions for nonlinear fractional differential-difference equations and systems. Copyright (C) 2014 JohnWiley& Sons, Ltd.