Existence of Mild Solutions for Fractional Neutral Functional Differential Equations

In several research works, controllability is one of the major concepts in mathematical control theory, which plays an important role in control systems. The controllability of nonlinear systems provided by evolution equations and qualitative theory of fractional differential equations has been developed. In this paper, we consider the initial value problems of fractional neutral functional differential equations. By applying fixed-point theorem, fractional calculus and controllability theory, a new set of acceptable conditions for approximate controllability of semi linear fractional differential equations are formulated and verified. Finally approximate controllability of semi linear fractional control differential systems is implied under the assumptions that the corresponding linear system is approximately controllable.