Time optimal control problem of a class of fractional distributed systems

In this paper, we consider a time optimal control problem of a system governed by a class of fractional semilinear evolution equations in the sense of the Caputo fractional derivative operator. The existence and uniqueness of mild solutions is proven. Then fractional time optimal control problem of the target varying with time is formulated. The existence of fractional time optimal controls is also presented. Finally, an example is given to illustrate the effectiveness of the results obtained.