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

被引：26
作者：
Antonio Taneco-Hernandez, Marco [1 ]
Vargas-De-Leon, Cruz [1 ,2 ]
机构：
[1] Univ Autonoma Guerrero, Fac Matemat, Av Lazaro Cardenas S-N, Chilpancingo 39087, Guerrero, Mexico
[2] Inst Politecn Nacl, Escuela Super Med, Plan San Luis & Diaz Miron S-N, Mexico City 11340, DF, Mexico
来源：
CHAOS SOLITONS & FRACTALS | 2020年 / 132卷
关键词：
Atangana-Baleanu fractional derivative; Direct Lyapunov method; Lyapunov functions; Lyapunov stability theory; HIV-AIDS epidemic system;
D O I：
10.1016/j.chaos.2019.109586
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 gamma is an element of (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). (C) 2019 Elsevier Ltd. All rights reserved.
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页数：9
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