Exact Solutions for Fractional Differential-Difference Equations by (G′/G)-Expansion Method with Modified Riemann-Liouville Derivative

Abstract

In this paper, the ($G′/G$)-expansion method is suggested to establish new exact solutions for fractional differential-difference equations in the sense of modified 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. With the aid of symbolic computation, we choose nonlinear lattice equations to illustrate the validity and advantages of the algorithm. It is shown that the proposed algorithm is effective and can be used for many other nonlinear lattice equations in mathematical physics and applied mathematics.