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Differential equations with random Gamma distributed moments of non-instantaneous impulses and p-moment exponential stability

Agarwal R., Hristova S., O’Regan D., Kopanov P.

Demonstratio Mathematica

2018

Vol. 51, nr 1

151--170

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.

On the controllability of fractional dynamical systems

Balachandran K., Kokila J.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 3

523-531

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.