Time delays occur so often in almost every situation, that to ignore them is to ignore reality. Time delays have a great influence on the stability and controllability of the system under consideration. As a consequence, the presence and the significant effects of time delays cannot be ignored. Indeed, the existence of delay makes the method of solution much more complicated. The purpose of this thesis is to introduce an efficient numerical scheme for solving delay fractional optimal control problems. The foundation of the proposed approach is based on a hybrid of block-pulse functions and orthonormal Taylor polynomials. Combining the two mentioned bases provides a flexible framework for solving the problem under consideration. The developed framework is flexible as the order of block-pulse functions and the degree of the orthonormal Taylor polynomials can be chosen arbitrarily.