Homotopy Analysis Transform Method for Integro-Differential Equations

In this article, we propose a reliable combination between the homotopy analysis method (HAM) and Laplace transformation method (LTM) to find the analytic approximate solution for integro-differential equations. This study represents significant features of HATM and its capability of handling integro-differential equations. Some illustrative examples are also presented to demonstrate the validity and applicability of this technique. Comparison between the obtained results by HATM and exact solution are shown integro-differential equations to illustrate the effective of this method. This method is reliable and capable of providing analytic treatment for solving such equations.