Numerical Method For Approximate Solutions of Fractional Differential Equations with Time Delay

Abstract

Due to the easy adaption of radial basis functions (RBFs), a directRBF collocation method is considered to develop an approximate scheme to solvefractional delay differential equations (FDDEs). The method of RBFs is a method of scattered data interpolation that has many application in different fields. 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. Applications to a variety ofproblems confirm that the proposed method is slightly more efficient than thoseintroduced in other literature and the convergence rate of our approach is high.

Keywords

• fractional delay differential equation
• radial basis function
• direct method
• collocation method