TY - JOUR
T1 - Stability and Lyapunov functions for systems with Atangana–Baleanu Caputo derivative
T2 - An HIV/AIDS epidemic model
AU - Taneco-Hernández, Marco Antonio
AU - Vargas-De-León, Cruz
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2020/3
Y1 - 2020/3
N2 - 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).
AB - 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).
KW - Atangana–Baleanu fractional derivative
KW - Direct Lyapunov method
KW - HIV–AIDS epidemic system
KW - Lyapunov functions
KW - Lyapunov stability theory
UR - http://www.scopus.com/inward/record.url?scp=85078175968&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2019.109586
DO - 10.1016/j.chaos.2019.109586
M3 - Artículo
SN - 0960-0779
VL - 132
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 109586
ER -
