Reproducing kernel method to solve fractional delay differential equations

Abstract

This paper is devoted to the numerical scheme for Fractional Delay Differential Equations (FDDEs). We use a semi-analytical method as Reproducing kernel Method (RKM) to solve FDDE such that the obtained approximate results are much better than other methods in comparison. The main obstacle to solve this problem is the existence of a Gram-Schmidt orthogonalization process in the general form of reproducing kernel method, that is very time consuming. So, we introduce a different implementation for the general form of the reproducing kernel method. In this method, the Gram-Schmidt orthogonalization process is eliminated to significantly reduce the CPU-time. Also, this new method, increases the accuracy of approximate solutions. Due to the increasing accuracy of approximate solutions, we will be able to provide a valid error analysis for this technique. The accuracy of the theoretical results are also illustrated by solving two numerical examples.