An Approximate Method for Solving Fractional Delay Differential Equations

Abstract

This paper presents an approximate method for solving a kind of fractional delay differential equations defined in terms of Caputo fractional derivatives. The approximate method is based on the application of the Bernstein’s operational matrix of fractional differentiation. First, Bernstein operational matrix of fractional differentiation is presented generalizing the idea of Bernstein’s operational matrix of derivative for integer orders, and then applied to solve the nonlinear fractional delay differential equations. The operational matrix method combined with the typical tau method reduces the fractional delay differential equation into system of nonlinear equations. Solving these nonlinear equations the desired solution is achieved. Two different cases of the fractional delay differential equations are illustrated and solved using the presented method. Numerical results and discussions demonstrate the applicability of the proposed method.