Fractional delay differential equations (FDDEs) are widely used in ecology, physiology, physical Sciences and many other areas of applied science. Fractional Delay differential equations usually do not have analytic solutions and can only be solved by some numeric methods. In this paper, a new method, which is generalized from finite difference method, has been provided to solve the delay differential equations. It has been used for numerical solution of such models and used for solving a number of problems such as the problem of the impact of food on the population changes of an area [1], the problem of the fluctuations of the population of adults in an area per time [2], the problem of the number of blood cells in humans [3] and the problem of the effect of noise on light which is reflected from laser to mirror [4]. The proposed method, besides being simple, is so exact and sensible in the solved problems

This article presents a numerical method based on the Adams–Bashforth–Moulton scheme to solve variable-order fractional delay differential equations (VFDDEs). In these equations, the variable-order (VO) fractional derivatives are described in the Caputo sense. The existence and uniqueness of the solutions are proved under Lipschitz condition. Numerical examples are presented showing the applicability and efficiency of the novel method.