Contrôlabilité approchée des équations différentielles impulsives avec dérivée fractionnaire de Caputo

Abstract

In this thesis, we study the approximate controllability for a class of Caputo fractional order impulsive differential equations under the assumption that the corresponding linear impulsive differential equation is approximately controllable. Based on fractional calculus, semi group theory, fixed point theorem and the technique of controllability theory, sufficient conditions for the approximate controllability of the fractional impulsive differential equation in the sense of Caputo are considered. Finally, we presented an applied example that illustrates the theoretical side of our study.