Numerical Solution of Time Fractional Coupled Korteweg-de Vries Equation with a Caputo Fractional Derivative in Two Parameters

This paper is devoted to constructing an analytical solution for a time-fractional coupled Korteweg-de Vries differential equations using a Caputo definition with two parameters, namely Dα,ρ. The homotopy analysis method is utilized to construct a new framework that obtained an analytic solution for fractional coupled Korteweg-de Vries equation with two parameters. We study the effect of the new parameter ρ on the solution. The new parameter ρ can play a significant effect on the solution behaviors. The results are compared with the exact solution in the case of standard derivative, natural decomposition method, and spectral collection method in the case of the fractional derivative with ρ = 1. A comparison study is given to validate the efficiency and accuracy of the proposed algorithm.