We consider the control systems governed by semilinear differential equations with Riemann-Liouville fractional derivatives in Banach spaces. Firstly, by applying fixed point strategy, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of fractional infinite dimensional control systems. Then, by using generally mild conditions of cost functional, we extend the existence result of optimal controls to the Riemann-Liouville fractional control systems. Finally, a concrete application is given to illustrate the effectiveness of our main results.
"Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations." Abstr. Appl. Anal. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/216919