Controllability Problems For Fractional Neutral Evolution Equations

Recently, The theory of fractional differential equations has been a valuable tool in the modeling of many phenomena in various fields of science. Although there has been a significant development in the theory, there still exists some fields that haven't been researched.In this paper, we study the complete controllability of a class of fractional neutral evolution equations with Caputo derivative in Banach spaces and the approximate controllability of the fractional neutral evolution equations in Hilbert spaces. In chapter 2, we have taken advantage of fractional power of operators, two new characteristic solution operators and their properties and Krasnoselskii's fixed point theorem, sufficient conditions of complete controllability of the desired problem are presented. In chapter 3, by using fixed point theorem, we derive a new set of sufficient conditions for the approximate controllability of the system under the assumption that the corresponding linear system is approximately controllable.