Numerical Method for Approximate Solutions of Fractional Differential Equations with Time-Delay

Due to the easy adaption of radial basis functions (RBFs), a direct RBF collocation method is considered to develop an approximate scheme to solve fractional delay differential equations (FDDEs). In spite of easy implementation of other high-order methods and finite difference schemes for solving a problem of fractional order derivatives, the challenge of these methods is their limited accuracy, locality, complexity and high cost of computing in discretization of the fractional terms, which suggest that global scheme such as RBFs that are more accurate way for discretizing fractional calculus and would allow us to remove the ill-conditioning of the system of discrete equations. So, the proposed approach, either employ any global RBFs for interpolating technique or uses arbitrary points for discretization, offers a very flexible framework for solving FDDEs. Applications to a variety of problems confirm that the proposed method is slightly more efficient than those introduced in other literatures and the convergence rate of our approach is high.