Publication Title On Approximate Solutions of a Fractional Chemotaxis-Haptotaxis Model via two Computational Schemes Download PDF
Publication Type journal
Publisher Nigerian Research Journal of Engineering and Environmental Sciences 6(1) 2021 pp. 236-247
Publication Authors * 1Okposo, N.I., 2Okposo, E.N. and 1Ossaiugbo, M.I
Year Published 2021-09-09
Abstract In this paper, the q-homotopy analysis transform method (qHATM) 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.
Publication Title Existence of solutions and stability analysis for a fractional helminth transmission model within the framework of Mittag-Leffler kernel Download PDF
Publication Type journal
Publisher Nigerian Journal of Science and Environment, Vol.19 (1) (2021)
Publication Authors Newton I. Okposo1*, Abel M. Jonathan1 , Emamuzo N. Okposo2 and Marcus Ossaiugbo1
Year Published 2021-10-10
Abstract In recent years, the many tools from fractional calculus have been extensively used in the mathematical modeling of infectious diseases. In this paper, an integer order helminth transmission model proposed by Lambura et al. is extended to a fractional model by incorporating the fractional Atangana-BaleanuCaputo derivative. Certain basic features such as non-negativity of solutions, invariant region within which the model equations are epidemiologically meaningful as well as equilibrium points and basic reproduction number are explored. Furthermore, the existence, uniqueness and Ulam-Hyers of the associated fractional model are explored via a fixed point technique and generalized Gronwall inequality.
Publication Title A mathematical study on a fractional COVID-19 transmission model within the framework of nonsingular and nonlocal kernel
Publication Type journal
Publisher Chaos, Solitons and Fractals 152 (2021) 111427
Paper Link https://doi.org/10.1016/j.chaos.2021.111427
Publication Authors Newton I. Okposoa,? , Matthew O. Adewole b,c , Emamuzo N. Okposo d, Herietta I. Ojarikrea , Farah A. Abdullahc
Year Published 2021-08-08
Abstract In this work, a mathematical model consisting of a compartmentalized coupled nonlinear system of fractional order differential equations describing the transmission dynamics of COVID-19 is studied. The fractional derivative is taken in the Atangana-Baleanu-Caputo sense. The basic dynamic properties of the fractional model such as invariant region, existence of equilibrium points as well as basic reproduction number are briefly discussed. Qualitative results on the existence and uniqueness of solutions via a fixed point argument as well as stability of the model solutions in the sense of Ulam-Hyers are furnished. Furthermore, the model is fitted to the COVID-19 data circulated by Nigeria Centre for Disease Control and the two-step Adams-Bashforth method incorporating the noninteger order parameter is used to obtain an iterative scheme from which numerical results for the model can be generated. Numerical simulations for the proposed model using Adams-Bashforth iterative scheme are presented to describe the behaviors at distinct values of the fractional index parameter for of each of the system state variables. It was shown numerically that the value of fractional index parameter has a significant effect on the transmission behavior of the disease however, the infected population (the exposed, the asymptomatic infectious, the symptomatic infectious) shrinks with time when the basic reproduction number is less than one irrespective of the value of fractional index parameter..
Publication Title Solutions for time-fractional coupled nonlinear Schrödinger equations arising in optical solitons
Publication Type journal
Publisher Chinese Journal of Physics 77 (2022) 965–984
Paper Link https://doi.org/10.1016/j.cjph.2021.10.014
Publication Authors Newton I. Okposo a,?,1 , P. Veeresha b,1 , Emamuzo. N. Okposo c,1
Year Published 2022-09-09
Abstract In this work, an efficient novel technique, namely, the ????-homotopy analysis transform method (????-HATM) is applied to obtain analytical solutions for a system of time-fractional coupled nonlinear Schrödinger (TF-CNLS) equations with the time-fractional derivative taken in the Caputo sense. This system of equations incorporate nonlocality behaviors which cannot be modeled under the framework of classical calculus. With numerous important applications in nonlinear optics, it describes interactions between waves of different frequencies or the same frequency but belonging to different polarizations. We first establish existence and uniqueness of solutions for the considered time-fractional problem via a fixed point argument. To demonstrate the effectiveness and efficiency of the ?????HATM, two cases each of two time-fractional problems are considered. One important feature of the ?????HATM is that it provides reliable algorithms which can be used to generate easily computable solutions for the considered problems in the form of rapidly convergent series. Numerical simulation are provided to capture the behavior of the state variables for distinct values of the fractional order parameter. The results demonstrate that the general response expression obtained by the ?????HATM contains the fractional order parameter which can be varied to obtain other responses. Particularly, as this parameter approaches unity, the responses obtained for the considered fractional equations approaches that of the corresponding classical equations.