Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381(2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic,trigonometric and rational, which have not been reported before.