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Bessel-quasilinearization technique to solve the fractional-order HIV-1 infection of CD4+ T-cells considering the impact of antiviral drug treatment

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  • Yüzbaşı, Şuayip
  • Izadi, Mohammad

Abstract

In this paper, two numerical methods based on the novel Bessel polynomials are developed to solve the fractional-order HIV-1 infection model of CD4+ T-cells considering the impact of antiviral drug treatment. In first of these methods, by using the Bessel polynomial and collocation points, we transform the HIV problem into a system of nonlinear algebraic equations. And this method, which is the method of direct solution is called as Bessel matrix method. The second method, which is called the Bessel-QLM method converts firstly HIV problem to a sequence of linear equations by using the technique of quasilinearization and then the reduced problem is solved by the direct Bessel matrix method. Error and convergence analysis are studied for the Bessel method. Finally, the applications are made on the numerical examples and also the numerical results are compared with the results of other available techniques. It is observed from applications that the presented results are better than the results of other existing methods and also the Bessel-QLM method is more efficient than the direct Bessel method.

Suggested Citation

  • Yüzbaşı, Şuayip & Izadi, Mohammad, 2022. "Bessel-quasilinearization technique to solve the fractional-order HIV-1 infection of CD4+ T-cells considering the impact of antiviral drug treatment," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322003939
    DOI: 10.1016/j.amc.2022.127319
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    References listed on IDEAS

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    1. Nazir, Ghazala & Shah, Kamal & Debbouche, Amar & Khan, Rahmat Ali, 2020. "Study of HIV mathematical model under nonsingular kernel type derivative of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Saadatmandi, Abbas & Sanatkar, Zeinab, 2018. "Collocation method based on rational Legendre functions for solving the magneto-hydrodynamic flow over a nonlinear stretching sheet," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 193-203.
    3. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
    4. Izadi, Mohammad & Srivastava, H.M., 2021. "An efficient approximation technique applied to a non-linear Lane–Emden pantograph delay differential model," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    5. Fazal Haq & Muhammad Shahzad & Shakoor Muhammad & Hafiz Abdul Wahab & Ghaus ur Rahman, 2017. "Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-7, December.
    6. Izadi, Mohammad, 2021. "A discontinuous finite element approximation to singular Lane-Emden type equations," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    7. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Abdel-Aty, Abdel-Haleem & Khater, Mostafa M.A. & Dutta, Hemen & Bouslimi, Jamel & Omri, M., 2020. "Computational solutions of the HIV-1 infection of CD4+T-cells fractional mathematical model that causes acquired immunodeficiency syndrome (AIDS) with the effect of antiviral drug therapy," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    9. Mohammad Izadi & Şuayip Yüzbaşi & Samad Noeiaghdam, 2021. "Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    10. Panwar, Virender Singh & Sheik Uduman, P.S. & Gómez-Aguilar, J.F., 2021. "Mathematical modeling of coronavirus disease COVID-19 dynamics using CF and ABC non-singular fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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    1. Mohammad Izadi & Mahmood Parsamanesh & Waleed Adel, 2022. "Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System," Mathematics, MDPI, vol. 10(23), pages 1-26, December.

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