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

Abstract

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.