AN INSTABILITY THEOREM FOR NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEMS.

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{λ∊ℂ {0}:ǀ arg (λ) ǀ < απ/2},where α ∊ (0, 1) is the order of the fractional differential system, then the equilibrium of the nonlinear system is unstable. [ABSTRACT FROM AUTHOR]