Abstarct: Fractional optimal control problems are problems that their associated dynamical systems have derivatives and integrals of fractional order. These derivatives and integrals provide more accurate models for existing systems in nature. Due to the necessity of solving problems and the high capability of neural network models, which are one of the active and useful fields in the area of artificial intelligence, in this thesis we study a fractional optimal control problem with equality and inequality constraints. In order to solve these problems, we use numerical methods baxsed on the perceptron neural network and Grunwald–Letnikov approximation, the neural network baxsed on the Mitag-Lefler function, the neural network baxsed on the fractional power series and also the neural network baxsed on Legendre polynomials. On the other hand, some of the fractional optimal control problems have the time-dependent fractional derivatives which in this thesis, we will also solve these kinds of problems.