Semi‐Analytical Solutions of the Multi‐Dimensional Time‐Fractional Solitary Water Wave Equations Using RPS Method

ABSTRACT This article concerns the use of the residual power series (RPS) approach to get the semi‐analytical solutions of multi‐dimensional Korteweg‐de Vries (KdV), that is, shallow water wave equations with any arbitrary time‐fractional order ( ). The time‐fractional derivative is considered in the Caputo sense. The solutions of the fractional KdV equation obtained using the RPS method for are compared with the exact solutions of the integer‐order KdV equation to show the RPS method's effectiveness, accuracy, and convergence. Some examples are also solved to study the effects of the fractional derivative on the wave's amplitude.