APPLICATION OF HOMOTOPY ANALYSIS TRANSFORM METHOD TO FRACTIONAL BIOLOGICAL POPULATION MODEL

Abstract

In this paper, we present an algorithm of the homotopy analysis transform method (HATM) which is a combination of Laplace transform method and the homotopy analysis method (HAM) to solve generalized biological population models. The fractional derivatives are described by Caputo sense. The proposed method presents a procedure of constructing the set of base functions and gives the high-order deformation equations in a simple form. The proposed scheme provides the solution in the form of a rapidly convergent series. Three examples are used to illustrate the preciseness and effectiveness of the proposed method. The results show that the HATM is very efficient, simple and can be applied to other nonlinear problems.