New reliable modifications of HPM and HAM

Abstract

In this article, a new modification of the homotopy perturbation method (HPM) and homotopy analysis method (HAM) is presented and applied to non-homogeneous fractional Volterra integro-differential equations with boundary conditions. A comparative study between the new modified homotopy perturbation method (MHPM) and the new modified homotopy analysis method (MHAM). Several illustrative examples are given to demonstrate the effectiveness and reliability of the methods.