He’s homotopy perturbation method with modification for solving multi-higher nonlinear Fredholm integro-differential equations of fractional order

Abstract

The aim of this paper is to present He’s Homotopy Perturbation Method (HPM) with Modification (MHPM) which are the semi-analytical technique and applying it to solve the Fredholm-Hammerstein type of multi-higher order nonlinear integro-fractional differential equations with variable coefficients and under given mixed conditions. The fractional derivative is described in the Caputo sense. This method is a combined form of the He’s polynomial with the Homotopy perturbation method and modification HPM. This technique enables us to find the exact solution of our nonlinear problems and extremely minimize the size of work. Some examples are given to illustrate the ability and reliability of this new techniques and the results reveal that the method is very simple, effective and yields a very rapid convergence of the solution series in most cases.