Description

The main aim of our thesis is to study the controllability analysis of a class of fractional differential inclusions/systems in Banach spaces. In this thesis, we have investigated the existence of the mild solutions for impulsive fractional differential inclusions involving the Caputo derivative in Banach spaces by using fractional calculation, operator semigroups, and Leray Schauder's fixed point theorem. Also, we have proved the controllability of impulsive fractional differential inclusions involving the Caputo derivative using Sectorial operator in Banach spaces. Next, we have studied the controllability result of the Cauchy problem for a fractional differential equation with delay in Banach spaces using the theory of analytic semigroups and confined in the Kuratowski measure of non-compactness and fixed point theorem. Moreover, we have proved the controllability of a class of impulsive fractional differential inclusions with nonlocal conditions by the Krasnoselskii theorem and the contraction mapping.