The proof of Lyapunov asymptotic stability theorems for Caputo fractional order systems

Clarivate, 2021 Matignon, 2005, Asymptotic stability of linear conservative systems when coupled with diffusive systems, ESAIM Control Optim. Calc. Var., 11, 487, 10.1051/cocv:2005016 Lakshmikantham, 2008, Time-varying Lyapunov functions and Lyapunov stability of nonautonomous fractional order systems, Commun. Appl. Anal., 12, 365 Li, 2009, Mittag–Leffler stability of fractional order nonlinear dynamic systems, Automatica, 45, 1965, 10.1016/j.automatica.2009.04.003 Delavari, 2012, Stability analysis of Caputo fractional-order nonlinear systems revisited, Nonlinear Dynam., 67, 2433, 10.1007/s11071-011-0157-5 Jarad, 2013, Stability of q-fractional non-autonomous systems, Nonlinear Anal. RWA, 14, 780, 10.1016/j.nonrwa.2012.08.001 Zhou, 2014, Stability criterion for a class of nonlinear fractional differential systems, Appl. Math. Lett., 28, 25, 10.1016/j.aml.2013.09.007 Liu, 2017, Asymptotical stability of Riemann–Liouville fractional neutral systems, Appl. Math. Lett., 69, 168, 10.1016/j.aml.2017.02.016 Du, 2019, Finite-time stability of a class of nonlinear fractional delay difference systems, Appl. Math. Lett., 98, 233, 10.1016/j.aml.2019.06.017 Wei, 2020, Mittag–Leffler stability of nabla discrete fractional order dynamic systems, Nonlinear Dynam., 101, 407, 10.1007/s11071-020-05776-3 Salahshour, 2020, A new Lyapunov stability analysis of fractional order systems with nonsingular kernel derivative, Alex. Eng. J., 59, 2985, 10.1016/j.aej.2020.03.040 Du, 2020, New criterion for finite-time stability of fractional delay systems, Appl. Math. Lett., 104, 10.1016/j.aml.2020.106248 Wei, 2021, Lyapunov stability theory for nonlinear nabla fractional order systems, IEEE Trans. Circuits Syst. II: Express Briefs, 68, 3246 Wei, 2021, Converse Lyapunov theorem for nabla asymptotic stability without conservativeness, IEEE Trans. Syst., Man, Cybern.: Syst. Chen, 2020 Liu, 2016, Lyapunov stability analysis of fractional nonlinear systems, Appl. Math. Lett., 51, 13, 10.1016/j.aml.2015.06.018 Agarwal, 2016, A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations, Fract. Calc. Appl. Anal., 19, 290, 10.1515/fca-2016-0017 Wei, 2019, Lyapunov functions for nabla discrete fractional order systems, ISA Trans., 88, 82, 10.1016/j.isatra.2018.12.016 Liu, 2019, Stability analysis for a class of nabla (q,h)-fractional difference equations, Turk. J. Math., 43, 664, 10.3906/mat-1811-96 Hinze, 2020, The direct method of Lyapunov for nonlinear dynamical systems with fractional damping, Nonlinear Dynam., 102, 1 Wei, 2021, Time-varying Lyapunov functions for nonautonomous nabla fractional order systems, ISA Trans. Wei, 2021, Fractional difference inequalities with their implications to the stability analysis of nabla fractional order systems, Nonlinear Dynam., 104, 3643, 10.1007/s11071-021-06451-x Zhou, 2021, What is the most suitable Lyapunov function?, Chaos, Solitons Fractals, 150, 10.1016/j.chaos.2021.111154 Naifar, 2017, Comments on Mittag–Leffler stability of fractional order nonlinear dynamic systems, Automatica, 75, 329, 10.1016/j.automatica.2016.09.023 Wu, 2021, Comments on “stability analysis of Caputo fractional-order nonlinear systems revisited”, Nonlinear Dynam., 104, 551, 10.1007/s11071-021-06279-5 Ma, 2001 Khalil, 2002 Wu, 2020, A general comparison principle for Caputo fractional-order ordinary differential equations, Fractals, 28, 10.1142/S0218348X2050070X Zhang, 2015, Stability analysis of a class of fractional order nonlinear systems with order lying in (0,2), ISA Trans., 56, 102, 10.1016/j.isatra.2014.12.006 Gallegos, 2019, Converse theorems in Lyapunov’s second method and applications for fractional order systems, Turk. J. Math., 43, 1626, 10.3906/mat-1808-75 Shen, 2014, Non-existence of finite-time stable equilibria in fractional order nonlinear systems, Automatica, 50, 547, 10.1016/j.automatica.2013.11.018