Linearized asymptotic stability for fractional differential equations
2016
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 $\{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\}$ where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
0
References
40
Citations
NaN
KQI