A Coupling Method of Homotopy Technique and Laplace Transform for Nonlinear Fractional Differential Equations

Abstract

In this work, the solutions of the fractional Sharma-Tasso-Olver (FSTO) and Fisher differential equations were investigated. The present study proposed a new novel and simple analytical method to obtain the solutions of FSTO and Fisher differential equations. Whereas, for nonlinear equations in general, no method is exists which yields to exact solution and therefore only approximate analytical solutions can be derived by using procedures such as linearization or perturbation. This method is combined form of the Laplace transformation and the Homotopy perturbation method. Advantage of the Laplace Homotopy Method (LHM), are simplicity of the computations, and non-requirement of linearization or smallness assumptions. For more illustration of the efficiency and reliability of LHM, some numerical results are depicted in different schemes and tables. Numerical results showed that the LHM was partly economical, efficient and precise to obtain the solution of nonlinear fractional differential equations.