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- Title
Extension of Lyapunov direct method about the fractional nonautonomous systems with order lying in $$\mathbf{(1,2)}$$.
- Authors
Guo, Yuxiang; Ma, Baoli
- Abstract
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.
- Subjects
CAPUTO fractional derivatives; LYAPUNOV functions; GRONWALL inequalities; SIMULATION methods &; models; STABILITY criterion
- Publication
Nonlinear Dynamics, 2016, Vol 84, Issue 3, p1353
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-015-2573-4