On the solution of fuzzy fractional optimal control problems with the Caputo derivative

This paper presents an extension to fractional optimal control problems with ambiguity. As the ambiguity is modeled with fuzzy method, we encounter with a fuzzy fractional optimal control problem. The objective in fuzzy fractional optimal control problem is to determine the best possible fuzzy control which satisfies the related fuzzy fractional dynamic systems and minimizes the fuzzy performance index. Here, the fractional derivative is described in the Caputo sense. To find the solution, first we state some definitions and prove some required theorems. Then, we employ the obtained result to determine the necessary conditions. Furthermore, we show that the obtained necessary optimality conditions become sufficient by considering some extra assumptions. Finally, some examples are presented for more illustration of the subject.