Solve the Initial Value Problems of Fractional Order Using The Homotopy Analytical Method and Improve Them Using Pade' Approximations

Abstract

In this research , the initial value problems of the caputo- fractional order are solved using the homotopy analysis method. The Pade' approximation is added to the fractional order to improve this method. The improvement is confirmed through two examples by comparing the value of mean square error for homotopy analysis method and the improved method.

Keywords

• homotopy analysis method (ham)
• pade' approximation (pa)
• mean square error(mse)