Algorithm for solving fractional partial differential equations using homotopy analysis method with Padé approximation

In recent years nonlinear problems have several methods to be solved and utilize a well-known analytic tools such as homotopy analysis method. In general, homotopy analysis method had gain a wide focus and improvement especially in typical nonlinear problem. The aim of this paper is to use homotopy method of analysis to solve partial differential equation in addition to improve method’s efficiency. The method in this paper is to apply approximation to Padé approach to obtain sufficient efficiency. As a result, the improvement has been verified by solving two cases beside a mean value comparison of the homotopy analysis method’s squared error with the improved form