Approximate Solution of Homogeneous and Nonhomogeneous 5αth-Order Space-Time Fractional KdV Equations

Abstract

In this paper, the semi-inverse method is applied to derive the Lagrangian of the [Formula: see text]th Korteweg de Vries equation (KdV). Then the time and space differential operators of the Lagrangian are replaced by corresponding fractional derivatives. The variation of the functional of this Lagrangian is devoted to lead the fractional Euler Lagrangian via Agrawal’s method, which gives the space-time fractional KdV equation. Jumarie derivative is used to obtain the space-time fractional KdV equations. The homotopy analysis method (HAM) is applied to solve the derived space-time fractional KdV equation. Then numerical solutions are compared with the known analytical solutions by tables and figures.