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The Riccati Sub-ODE Method For Fractional Differential-difference Equations

In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applications, we apply this method to solve the two-component fractional Volterra lattice equations and the fractional m-KdV lattice equation. Some new exact solutions for the two fractional differential-difference equations are obtained.