Yazar "Khan, Muhammad Altaf" seçeneğine göre listele

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    Conformable derivative: A derivative associated to the Riemann-Stieltjes integral
    (Natural Sciences Publishing, 2022) Atangana, Abdon; Akgül, Ali; Khan, Muhammad Altaf; Ibrahim, Rabha Waell
    In mathematics, the Riemann-Stieltjes integral (Formula Presented) is known to be the more general version of the well-known Riemann integral that is used in classical integral calculus. This integral has found application in several fields. However, there is no clear derivative associate to the generalized integral, except the concept of global derivative that was suggested very recently. Nevertheless, a more generalized differential operator called conformable derivative was suggested and many concerns have been raised as what such operator cannot be considered as derivative. In this paper, we proved that not only the operator is a derivative but a derivative associate to the well-known Riemann-Stieltjes integral. We have in addition present some applications of the conformable derivative in image processing and dynamical processes including chaos and epidemiology © 2022. NSP Natural Sciences Publishing Cor
  • [ X ]
    Öğe
    The analysis of a new fractional model to the Zika virus infection with mutant
    (Cell Press, 2024) Zafar, Zain Ul Abadin; Khan, Muhammad Altaf; Inc, Mustafa; Akgul, Ali; Asiri, Mohammed; Riaz, Muhammad Bilal
    We present a new mathematical model to analyze the dynamics of the Zika virus (ZV) disease with the mutant under the real confirmed cases in Colombia. We give the formulation of the model initially in integer order derivative and then extend it to a fractional order system in the sense of the Mittag-Leffler kernel. We study the properties of the model in the Mittag-Leffler kernel and establish the result. The basic reproduction of the fractional system is computed. The equilibrium points of the Zika virus model are obtained and found that the endemic equilibria exist when the threshold is greater than unity. Further, we show that the model does not possess the backward bifurcation phenomenon. The numerical procedure to solve the problem using the Atangana-Baleanu derivative is shown using the newly established numerical scheme. We consider the real cases of the Zika virus in Colombia outbreak are considered and simulate the model using the nonlinear least square curve fit and computed the basic reproduction number R0= 0.4942, whereas in previous work (Alzahrani et al., 2021) [1], the authors computed the basic reproduction number R0 = 0.5447. This is due to the fact that our work in the present paper provides better fitting to the data when using the fractional order model, and indeed the result regarding the data fitting using the fractional model is better than integer order model. We give a sensitivity analysis of the parameters involved in the basic reproduction number and show them graphically. The results obtained through the present numerical method converge to its equilibrium for the fractional order, indicating the proposed scheme's reliability.