Generalized fractional-order hybrid of block-pulse functions and Bernoulli polynomials approach for solving fractional delay differential equations

In the current study, we propose a systematize technique for solving fractional delay differential equations in the Caputo sense. Therefore, we compute an exact Riemann–Liouville fractional integral operator for the generalized fractional-order hybrid of block-pulse functions and Bernoulli polynomials, and we use it in order to reduce the fractional delay differential equations into a system of algebraic equations. The last ones are solved numerically using the Newton’s iterative method. The relative simplicity of the procedure together with the accuracy of the results is the essential feature of the present method. Finally, we conclude that for the same problems, our results are better than other results presented in the literature.