Abstarct: ‎‎In ‎the ‎world ‎where ‎we ‎live‎, some dynamic and physical laws are not expressed in general dynamical systems. For modelling complex systems or when the particles are in microscopic scales, the use of fractional order systems seems to be essential. On the other hand, dynamic movements which preserve the memory and transmitter hereditary effects and complex dynamics such as playback and release the gas, or distribution of heat in a non-homogeneous environment with high emission which are commonly modeled with fractional differential equations. Optimal control problems with integer order derivatives include a huge area of research about control and optimal control. This subject has been researched in science and technology for a long time. Fractional optimal control problems are actually the same optimal control problems that their associate dynamical systems are fractional dynamic systems. During recent years, due to the above discussed matters, optimal fractional was born and grew up. Among many different methods, in this thesis, we use an optimization method baxsed on Jacobi polynomials. ‎Using a collocation method and transforming the problem into a nonlinear programming problem and solving it by a specialized optimization software, the solutions of the orginal problem will be obtained. ‎Also, some numerical examples are presented to confirm the effectiveness of the method for solving fractional optimal control problems.