Optimal Control Problems Governed by Fractional Differential Equations with Control Constraints

A class of optimal control problems governed by fractional differential equations with control constraints and free right end point is considered. We first prove a result on the existence of optimal solutions for the case where the state equation may be nonlinear in control variable. Then we establish first- and second-order optimality conditions for locally optimal solutions to the general problem. When $\frac{1}2<\alpha<1$, a theory of no-gap second-order conditions is obtained. A result on regularity of optimal solution for the case where the state equation is linear in control variable is also given.