An Approximate Analytical Solution of the Family of Time-Fractional KdV Equations

Abstract

The classical KdV equation has been found to describe a large number of physical phenomena. In this paper, we consider the homotopy perturbation method (HPM) for obtaining the approximate analytical solution of time-fractional KdV equations (TFKdVEs). In the KdV equation, the time derivative will be replaced by a fractional derivative α, where 0 α ≤ 1. The initial approximation can be determined by imposing the initial conditions. Numerical examples show that the numerical results of TFKdVEs can be obtained within a few iterations.