Travelling wave solutions for the time-fractional equations by the Sine-Gordon expansion method

Abstract

The aim of this paper is to explore travelling wave solutions by utilising the novel sine-Gordon expansion method for the time-fractional (1 + 1)-dimensional Hirota Satsuma equation and the time-fractional (2 + 1) -dimensional Caudrey-Dodd-GibbonKotera-Sawada equations. Using the traveling wave transformation, the fractional PDE turns into an ODE. Applying the auxiliary equation from the described method, we get an algebraic polynomial, setting the like power to zero, we get a system of algebraic equations. Solving these equations by using mathematical software program, we acquire the solution sets for the constants. Abundant travelling wave solutions are obtained and expressed in terms of hyperbolic functions. Some graphics of the solutions have also been presented. The proposed method is direct and effective in solving nonlinear evolution equations.