On Approximate Solutions of a Fractional Chemotaxis-Haptotaxis Model via two Computational Schemes

In this paper, the q-homotopy analysis transform method (q-HATM) and homotopy perturbation transform method (HPTM) were employed to obtain analytic series solutions for a coupled system of nonlinear time-fractional chemotaxis-haptotaxis model. The applied methods yielded solutions in the form of convergent series and does not involve discretization or linearization. Furthermore, the obtained analytical results were compared for both methods via graphical representations for distinct arbitrary order with a view to demonstrating the efficiency of the methods in handling even more complex nonlinear systems from mathematical biology