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arXiv · 1512.04989

Linearized Asymptotic Stability for Fractional Differential Equations

N. D. Cong·T. S. Doan·S. Siegmund·H. T. Tuan
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Abstract

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 $\{λ\in \C : |\arg λ| > \frac{απ}{2}\}$ where $α> 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable.

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N. D. Cong, T. S. Doan, S. Siegmund, H. T. Tuan. 2016-05-08. Linearized Asymptotic Stability for Fractional Differential Equations. https://arxiv.org/abs/1512.04989

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