Application of the ?−homotopy analysis transform method (?−HATM) to the solution of a fractional attraction Keller-Segel chemotaxis model

Abstract

The main purpose of this paper is to construct approximate analytic solutions for a time-fractional attraction Keller-Segel (TF-AKS) chemotaxis model using the ?−homotopy analysis transform method (?−HATM). The obtained results and numerical simulations for three sets of initial data describe the behavior of the system. This further assert the convenience, computational efficiency and wide applicability of the proposed method even to more complex coupled systems of partial differential equations arising from mathematical biology.