Extension of Lyapunov direct method about the fractional nonautonomous systems with order lying in \((1,2)\). (English) Zbl 1354.34018
Summary: In this paper, Lyapunov direct method is employed to study the stability problem of Caputo-type fractional nonautonomous systems with order between 1 and 2. By utilizing Riemann-Liouville fractional integral, some sufficient conditions on stability are derived. In the proof of the obtained results, Bellman-Gronwall’s inequality, the generalized Bihari inequality and estimates of Mittag-Leffler functions are employed. Besides, two examples and corresponding numerical simulations are provided to show the validity and feasibility of the proposed stability criterion.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 37B55 | Topological dynamics of nonautonomous systems |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
Keywords:
Caputo derivative; fractional nonautonomous systems; Bihari-type inequality; Bellman-Gronwall’s inequality; globally uniformly asymptotically stableReferences:
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