Abstarct: With the development and complexity of optimal control problems, new methods have to be developed to solve these issues. When dynamic systems are complex or have memory, movement and propagation are no longer followed by ordinary derivative laws. In such cases, movements follow the rules of the fractional order. Due to its many applications in science, engineering and medicine, delay systems have always been considered by researchers of various disciplines, and the non-locality of the fractional operator has led to a combination of these two issues and achieving better results. Since there is no exact solution for the delay fractional optimal control problem in general, over the past few years various numerical methods have been published in this regard. The choice of a numerical method proportional to the fractional derivative structure has always been one of the most important challenges in this field. In this thesis we study the fractional polynomials and provide a numerical method baxsed on the Muntz-Legendre polynomials to solve the delay fractional optimal control problems. Also, for comparing the proposed method and the structure of the solutions of the delayed problem, the block pulse functions and Haar wavelates have been investigated and compared with several numerical methods.