Discussing a Solution to Nonlinear Duffing Oscillator with Fractional Derivatives Using Homotopy Analysis Method (HAM)

Abstract

In this paper, we obtain an analytic solution to the initial valued problem of the Duffing oscillator with fractional order derivative. The Homotopy analysis method (HAM) was used to obtain the said analytic solution to the proposed initial valued problem. In order to achieve our goal, the problem was first converted to its augmented equivalent system of equations having the same order. The accuracy of the result obtained was demonstrated with an example and the solution illustrated graphical. For the excitation amplitude ? and the excitation frequency ?, it was observed that as they increase, the amplitude also increase. As the unit of time increases, it was observed that the system becomes more chaotic and this behaviour is not out of place.