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An instability theorem for nonlinear fractional differential systems

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  • 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.

    Mathematics Subject Classification: 34A08, 34K20.


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