Two reliable methods for solving the time fractional Clannish Random Walker's Parabolic equation

Abstract

In this paper, we study the exact solutions of nonlinear time fractional Clannish Random Walker's Parabolic (CRWP) equation. We extend the (G′/G) and (G′/G, 1/G)-expansion methods to fractional differential equations in the sense of modified Riemann–Liouville derivative based on fractional complex transformation. We obtained hyperbolic function solutions, trigonometric function solutions and rational function solutions. It was shown that the considered methods and transform are very reliable and efficient for these type fractional equations. These methods and transform can be used in studying many other nonlinear time and space fractional differential equations and nonlinear systems.