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Study of the Fractional-Order HIV-1 Infection Model with Uncertainty in Initial Data

Author

Listed:
  • Yong Wu
  • Shabir Ahmad
  • Aman Ullah
  • Kamal Shah
  • Nasser Hassen Sweilam

Abstract

Uncertainty always lives with us. We cannot take exact measurement of initial conditions or parameters values in a mathematical model. As humans, we are remaining alive in an environment where the uncertainties lie in the modelling of physical phenomena. There might be some incomplete information or estimation of the parameter or initial values. To handle uncertainty, we use fuzzy operators rather than classical operators. In this paper, we study a model of HIV-1 infection by taking uncertainty in the initial data under Caputo fractional operator. We explore the existence and uniqueness of the results through fixed-point theory. We study the Ulam–Hyres stability of the considered model. By using the fuzzy Laplace Adomian decomposition method, numerical results are obtained for specific fuzzy initial conditions. To better understand the behaviour of the fuzzy solution, we present the obtained numerical results graphically for various fractional orders where the uncertainty lies in [0, 1].

Suggested Citation

  • Yong Wu & Shabir Ahmad & Aman Ullah & Kamal Shah & Nasser Hassen Sweilam, 2022. "Study of the Fractional-Order HIV-1 Infection Model with Uncertainty in Initial Data," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-16, January.
    • Handle: RePEc:hin:jnlmpe:7286460
    DOI: 10.1155/2022/7286460
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    Cited by:

    1. Iskakova, Kulpash & Alam, Mohammad Mahtab & Ahmad, Shabir & Saifullah, Sayed & Akgül, Ali & Yılmaz, Gülnur, 2023. "Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 219-245.
    2. Shahram Rezapour & Sina Etemad & Ravi P. Agarwal & Kamsing Nonlaopon, 2022. "On a Lyapunov-Type Inequality for Control of a ψ -Model Thermostat and the Existence of Its Solutions," Mathematics, MDPI, vol. 10(21), pages 1-11, October.

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