Contribution to the study of the controllability of semilinear differential equations of fractional order

Abstract

In view of the increased interest that the Kalman concept has received since the 1960s, this thesis is dedicated to contributing to the development of research on the controllability of a class of semilinear differential systems of fractional order with the impulsive condition in abstract spaces, by applying the techniques of fixed point theory and concepts of semigroup theory and define an admissible set of necessary and sufficient conditions to prove the existence of mild solutions and are renewed in each time with what suits the studied system. During this doctoral thesis, we rely on the use of three different definitions of fractional derivatives and discuss their fundamental properties, as well as highlighting the most important basic mathematical principles and necessary theoretical concepts to reach the desired results. This thesis permeates a valuable set of practical examples to prove the proposed approach and further clarify the given purpose