Optimal Control Problem of Positive Solutions to Fractional Differential Equations

In this paper, we study the existence and uniqueness of positive solutions to fractional differential equations initial value problem, then we prove the existence of an optimal control that minimizes the nonlinear cost functional. At first, by using a fixed point theorem of a-concave operator, we establish the existence and uniqueness result of positive solutions for each given control function. Then, we consider the optimal control problem of positive solution to our system, and prove the existence of an optimal control. At last, an related example is given to demonstrate the application of our main results.