The Solvability and Optimal Controls of Impulsive Fractional Semilinear Differential Equations

In this paper, we deal with the impulsive control systems of fractional order and their optimal controls in Banach spaces. We firstly show the existence and uniqueness of mild solutions for a broad class of impulsive fractional infinite dimensional control systems under suitable assumptions. Then by using generally mild conditions of cost functionals, we extend the existence result of optimal controls to the impulsive fractional control systems. Finally, a concrete application is given to illustrate the effectiveness of our main results.