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Lyapunov functions for fractional-order systems in biology: Methods and applications

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  • Boukhouima, Adnane
  • Hattaf, Khalid
  • Lotfi, El Mehdi
  • Mahrouf, Marouane
  • Torres, Delfim F.M.
  • Yousfi, Noura

Abstract

We prove new estimates of the Caputo derivative of order α ∈ (0, 1] for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a fractional cellular model are studied. More precisely, we construct suitable Lyapunov functionals to demonstrate the global stability of the free and endemic equilibriums, for both fractional models, and we also perform some numerical simulations that confirm our choices.

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  • Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306202
    DOI: 10.1016/j.chaos.2020.110224
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    References listed on IDEAS

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