On Inhomogeneous Fractional Partial Differential Equations

Abstract

In this paper, a coupling method of Laplace transform and Homotopy analysis method is applied for solving various inhomogeneous fractional partial differential equations.The proposed algorithm presents a procedure of construct the base function and gives a high order deformation equation in simple form. The purpose of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in the other analytical techniques. The scheme is tested for some examples to demonstrate the capability of LHAM for fractional partial differential equations.

Keywords: Laplace homotopy analysis method; homotopy analysis method; fractional differential equations; modified Riemann-Liouville derivative; Wave equation; Burger’s equation; Klein-Gorden equation: