Abstarct: In present thesis, two direct and indirect methods have been considered to solve the fractional optimal control problems. In the indirect method, in order to approximate the existence variables at the Chebyshev-Gauss points, we introduce and utilize the fractional Lagrange interpolating function. Also, we express and prove the fractional necessary optimality conditions. In the direct method, we convert the fractional optimal control problem to a corresponding fractional calculus of variations problem. Then, by using the Clenshaw-Curtis formula and the Chebyshev-Gauss-Lobato points, we reduce the problem to a nonlinear programming problem. The organization of the present thesis is as follows. At first, we express the preliminaries and the needed conceptions. Then, we introduce the fractional optimal control problems. Also, we present and prove the fractional necessary optimality conditions. Next, we present the indirect method to solve the fractional optimal control problems. Afterward, we bring the direct method baxsed on Clenshaw-Curtis formula. Finally, the conclusions and the suggestions has been included in the last chapter.