| Autor: |
Nguyen Cong, Thai Doan, Stefan Siegmund, Hoang Tuan |
| Jazyk: |
angličtina |
| Rok vydání: |
2016 |
| Předmět: |
|
| Zdroj: |
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2016, Iss 39, Pp 1-13 (2016) |
| Druh dokumentu: |
article |
| ISSN: |
1417-3875 |
| DOI: |
10.14232/ejqtde.2016.1.39 |
| Popis: |
We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector $\{\lambda \in \mathbb{C} : |\arg \lambda| > \frac{\alpha \pi}{2}\}$ where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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