An instability theorem for nonlinear fractional differential systems

Abstract

In this paper, we give a criterion on instability of an equilibrium of nonlinear Caputo fractional differential systems. More precisely, we prove that if the spectrum of the linearization has at least one eigenvalue in the sector $$\left\{λ\in\C\setminus\{0\}:|\arg{(λ)}|<\frac{απ}{2}\right\},$$ where $\alpha \in (0,1)$ is the order of the fractional differential systems, then the equilibrium of the nonlinear systems is unstable.

18 pages

References in corpus (1)

• Linearized Asymptotic Stability for Fractional Differential Equations

Cited by in corpus (2)

• Generation of nonlocal fractional dynamical systems by fractional differential equations
• On asymptotic properties of solutions to fractional differential equations