Solving nonlinear fractional differential equations using multi-step homotopy analysis method

This paper presents a numerical technique for solving fractional differential equation by employing the multi-step homotopy analysis method (MHAM). It is known that the corresponding numerical solution obtained using the HAM is valid only for a short time. On the contrary, the results obtained using the MHAM are more valid and accurate during a long time, and are highly agreement with the exact solutions in the case of integer-order systems. The objective of the present paper is to modify the HAM to provide symbolic approximate solution for linear and nonlinear of fractional differential equations. The efficient and accuracy of the method used in this paper will be demonstrated by comparison with the known methods and with the known exact solutions in the non fractional case. The fractional derivatives are described in the Caputo sense.