Nonlinear differential equations with impulses occurring at random time and acting noninstantaneously on finite intervals are studied. We consider the case when the time where the impulses occur is Gamma distributed. Lyapunov functions are applied to obtain sufficient conditions for the p-moment exponential stability of the trivial solution of the given system.
This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.
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