# American Institute of Mathematical Sciences

October  2017, 22(8): 3079-3090. doi: 10.3934/dcdsb.2017164

## An instability theorem for nonlinear fractional differential systems

 1 Institute of Mathematics, Vietnam Academy of Science and Technology, Viet Nam 2 Department of Mathematics, Hokkaido University, Japan 3 Department of Mathematics, Technische Universität Dresden, Dresden, Germany

Received  August 2016 Revised  October 2016 Published  June 2017

In this paper, we give a criterion on instability of an equilibrium of a nonlinear Caputo fractional differential system. More precisely, we prove that if the spectrum of the linearization has at least one eigenvalue in the sector
 $\left\{ \lambda \in \mathbb{C}\setminus \{0\}:|\arg (\lambda )| < \frac{\alpha \pi }{2} \right\},$
where
 $α∈ (0,1)$
is the order of the fractional differential system, then the equilibrium of the nonlinear system is unstable.
Citation: Nguyen Dinh Cong, Doan Thai Son, Stefan Siegmund, Hoang The Tuan. An instability theorem for nonlinear fractional differential systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3079-3090. doi: 10.3934/dcdsb.2017164
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