Numerical approximation of the system of fractional differential equations with delay and its applications

In this paper, the system of fractional differential equations with delay is studied. The computational method based on the hybrid functions of the general block-pulse functions and Legendre polynomials is presented to obtain the numerical results for the solution of our problem. In fact, the system under study is converted to the corresponding nonlinear algebraic system of equations, which is resolved by using the collocation technique. Also, the error estimate for the suggested computational method that verifies the convergence is presented. Finally, we examine two models arising in engineering and applied science, including the Chen and human immunodeficiency viruses systems, to illustrate the efficiency of the method.