Homotopy Analysis Method for Solving Delay Differential Equations of Fractional Order

Abstract

In this paper, we implement the Homotopy Analysis method for solving numerically non-linear delay differential equations of fractional order. The fractional derivative will be in the Caputo sense. In this approach, the solutions are found in the form of a convergent power series with easily computed components. Some numerical examples are presented to illustrate the accuracy and ability of the proposed method.

Keywords: Homotopy Analysis method, delay differential equations, fractional calculus, fractional delay differential equations.