Lyapunov functions for fractional-order systems in biology: Methods and applications
Adnane Boukhouima,
Khalid Hattaf,
El Mehdi Lotfi,
Marouane Mahrouf,
Delfim F.M. Torres and
Noura Yousfi
Chaos, Solitons & Fractals, 2020, vol. 140, issue C
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.
Keywords: Nonlinear ordinary differential equations; Fractional calculus; Caputo derivatives; Lyapunov analysis; Stability; Mathematical biology (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306202
DOI: 10.1016/j.chaos.2020.110224
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