Stability and Lyapunov functions for systems with Atangana–Baleanu Caputo derivative: An HIV/AIDS epidemic model

Marco Antonio Taneco-Hernández and Cruz Vargas-De-León

Chaos, Solitons & Fractals, 2020, vol. 132, issue C

Abstract: In this paper, we derive extensions of classical Lyapunov and Chetaev instability theorems and LaSalle’s invariance principle to the case of Atangana–Baleanu derivative in the Caputo sence. Moreover, we get some results to estimates fractional derivatives of quadratic and Volterra–type Lyapunov functions when γ ∈ (0, 1). Finally, we present rigorous proofs about the complete classification for global dynamics of an HIV/AIDS epidemic model with Atangana–Baleanu Caputo derivative (Chaos, Solitons and Fractals 126 (2019) 41–49).

Keywords: Atangana–Baleanu fractional derivative; Direct Lyapunov method; Lyapunov functions; Lyapunov stability theory; HIV–AIDS epidemic system (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305430

DOI: 10.1016/j.chaos.2019.109586

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