New solutions of the time-fractional Hirota–Satsuma coupled KdV equation by three distinct methods

Abstract

In this paper, new solutions of the time-fractional Hirota–Satsuma coupled KdV equation model the intercommunication between two long waves that have well-defined dispersion connection received successfully by the unified method, the improved [Formula: see text]-expansion method and the homogeneous balance method. In contrast, these methods are simple and efficient, and can obtain different exact solutions to this equation. By symbolic calculation, polynomial solutions, hyperbolic function solutions, trigonometric function solutions, rational function solutions, etc. are acquired. Furthermore, we plot and analyze some solutions.