An Efficient Numerical Scheme for Solving a Fractional-Order System of Delay Differential Equations.

Fractional order systems of delay differential equations are very advantageous in analyzing the dynamics of various fields such as population dynamics, neural networking, ecology, and physiology. The aim of this paper is to present an implicit numerical scheme along with its error analysis to solve a fractional-order system of delay differential equations. The proposed method is an extension of the L1 numerical scheme and has the error estimate of O ( h 2 ) , where h denotes the step size. Further, we solve various non-trivial examples using the proposed method and compare the results with those obtained by some other established methods such as the fractional Adams method and the three-term new predictor-corrector method. We observe that the proposed method is more accurate as compared to the fractional Adams method and the new predictor-corrector method. Moreover, it converges for very small values of the order of fractional derivative.