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Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes

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  • Tuan Hoang, Manh
  • Nagy, A.M.

Abstract

In this paper, we propose and study a Logistic model with feedback control of fractional order that is extended directly from a system of ordinary differential equations. Uniform asymptotic stability of this model is established based on an appropriate Lyapunov function and an important consequence of this result; we present a simple proof for the global stability of the original system of ordinary differential equations. Besides, to numerically solve and simulate the proposed fractional model, unconditionally positive nonstandard finite difference schemes are constructed and analyzed. Finally, the numerical simulations obtained by the constructed nonstandard finite difference schemes are compared with the Grunwald–Letnikov scheme to reveal that the proposed scheme is convenient for solving the proposed model and confirm the validity of the established results.

Suggested Citation

  • Tuan Hoang, Manh & Nagy, A.M., 2019. "Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 24-34.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:24-34
    DOI: 10.1016/j.chaos.2019.03.031
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    References listed on IDEAS

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    1. Hamdan, Nur ’Izzati & Kilicman, Adem, 2018. "A fractional order SIR epidemic model for dengue transmission," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 55-62.
    2. Dimitrov, Dobromir T. & Kojouharov, Hristo V., 2008. "Nonstandard finite-difference methods for predator–prey models with general functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(1), pages 1-11.
    3. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
    4. Arenas, Abraham J. & González-Parra, Gilberto & Chen-Charpentier, Benito M., 2016. "Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 48-63.
    5. Anguelov, Roumen & Lubuma, Jean M.-S., 2003. "Nonstandard finite difference method by nonlocal approximation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(3), pages 465-475.
    6. West, Bruce J., 2015. "Exact solution to fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 103-108.
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    Cited by:

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    4. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.

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