A new Chelyshkov matrix method to solve linear and nonlinear fractional delay differential equations with error analysis

In this paper, we investigate the possible treatment of a class of fractional-order delay differential equations. In delay differential equations, the evolution of the state depends on the past time, which increases the complexity of the model. The fractional term is defined in the Caputo sense, and to find its solution we discretize the unknown solution using a truncated series based on orthogonal Chelyshkov functions. Then, the resulting system in terms of the unknown coefficients is solved that guarantees to produce highly accurate solutions. A detailed error analysis for the proposed technique is studied to give some insight into the error bound of the proposed technique. The method is then tested on some examples to verify the efficiency of the proposed technique. The method proves the ability to provide accurate solutions in terms of error and computational cost and through some comparisons with other related techniques. Thus, the method is considered a promising technique to encounter such problems and can be considered as an efficient candidate to simulate such problems with applications in science.