1-point fractional adams method for solving single order differential equations with fractional delay

This paper deals with fractional delay differential equations (FDDE) of single order with fractional Caputo derivatives using the 1-point fractional Adams method. The proposed method is a predictor-corrector approach that can be constructed from the Adams-Bashforth method and Adams-Moulton method to achieve both simplicity and accuracy. The implementation of the fractional Caputo derivatives using the Euler-Gamma function and the approximation of delay term using the Newton divided difference interpolation are discussed. Some of the numerical examples are presented to show the proposed method is reliable and efficient