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Study of HIV mathematical model under nonsingular kernel type derivative of fractional order

Author

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  • Nazir, Ghazala
  • Shah, Kamal
  • Debbouche, Amar
  • Khan, Rahmat Ali

Abstract

In this manuscript, we investigate existence theory as well as stability results to the biological model of HIV (human immunodeficiency virus) disease. We consider the proposed model under Caputo-Fabrizio derivative (CFD) with exponential kernel. We investigate the suggested model from other perspectives by using fixed point approached derive its existence and uniqueness of solution. Further the stability of the concerned solution in Hyers-Ulam sense is also investigated. Further to derive the approximate solution in the form of series to the considered model, we use integral transform of Laplace coupled with Adomian decomposition method. The concerned technique is powerful tool to find semi-analytical solutions to many nonlinear problems. Finally, we demonstrate the results of approximate solutions through graphs by using Matlab.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304926
    DOI: 10.1016/j.chaos.2020.110095
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    References listed on IDEAS

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    1. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Alan S. Perelson & Avidan U. Neumann & Martin Markowitz & John M. Leonard & David D. Ho, 1996. "HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time," Working Papers 96-02-004, Santa Fe Institute.
    3. Fathalla A. Rihan, 2013. "Numerical Modeling of Fractional-Order Biological Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, August.
    4. Khan, Aziz & Gómez-Aguilar, J.F. & Saeed Khan, Tahir & Khan, Hasib, 2019. "Stability analysis and numerical solutions of fractional order HIV/AIDS model," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 119-128.
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    Cited by:

    1. Tyagi, Swati & Martha, Subash C. & Abbas, Syed & Debbouche, Amar, 2021. "Mathematical modeling and analysis for controlling the spread of infectious diseases," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. 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).
    3. Hashem Najafi & Sina Etemad & Nichaphat Patanarapeelert & Joshua Kiddy K. Asamoah & Shahram Rezapour & Thanin Sitthiwirattham, 2022. "A Study on Dynamics of CD4 + T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-32, April.
    4. Asamoah, Joshua Kiddy K. & Fatmawati,, 2023. "A fractional mathematical model of heartwater transmission dynamics considering nymph and adult amblyomma ticks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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