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On Analysis Of Fractional Order Mathematical Model Of Hepatitis B Using Atangana–Baleanu Caputo (Abc) Derivative

Author

Listed:
  • ANWARUD DIN

    (Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China)

  • YONGJIN LI

    (Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China)

  • FAIZ MUHAMMAD KHAN

    (��Department of Mathematics and Statistics, University of Swat, Swat, KP, Pakistan)

  • ZIA ULLAH KHAN

    (��Department of Mathematics and Statistics, University of Swat, Swat, KP, Pakistan)

  • PEIJIANG LIU

    (��School of Statistics and Mathematics, Guangdong University of Finance and Economics, Big data and Educational Statistics Application Laboratory, Guangzhou 510320, P. R. China§School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China)

Abstract

The scaling exponent of a hierarchy of cities used to be regarded as a fractional. This paper investigates a newly constructed system of equation for Hepatitis B disease in sense of Atanganaa–Baleanu Caputo (ABC) fractional order derivative. The proposed approach has five distinctive quantities, namely, susceptible, acute infections, chronic infection, immunized and vaccinated populace. By applying some well-known results of fixed point theory, we find the Ulam–Hyers type stability and qualitative analysis of the candidate solution. The deterministic stability for the proposed system is also computed. We apply well-known transform due to Laplace and decomposition techniques (LADM) and Adomian polynomial for nonlinear terms for computing the series solution for the proposed model. Graphical results show that LADM is an efficient and robust method for solving nonlinear problems.

Suggested Citation

  • Anwarud Din & Yongjin Li & Faiz Muhammad Khan & Zia Ullah Khan & Peijiang Liu, 2022. "On Analysis Of Fractional Order Mathematical Model Of Hepatitis B Using Atangana–Baleanu Caputo (Abc) Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-18, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400175
    DOI: 10.1142/S0218348X22400175
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    Citations

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    Cited by:

    1. Sabir, Zulqurnain & Said, Salem Ben & Baleanu, Dumitru, 2022. "Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Yaagoub, Zakaria & Allali, Karam, 2022. "Fractional HBV infection model with both cell-to-cell and virus-to-cell transmissions and adaptive immunity," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. El-Mesady, A. & Elsonbaty, Amr & Adel, Waleed, 2022. "On nonlinear dynamics of a fractional order monkeypox virus model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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