Simplified reproducing kernel method for fractional differential equations with delay

Abstract

This paper is devoted to the numerical scheme for the delay initial value problems of a fractional order. The main idea of this method is to establish a novel reproducing kernel space that satisfies the initial conditions. Based on the properties of the new reproducing kernel space, the simplified reproducing kernel method (SRKM for short) is applied to obtain accurate approximation. The Schmidt orthogoralization process which requires a large number of calculation is less likely to be employed. Numerical experiments are provided to illustrate the performance of the method.