Series solutions of a fractional oscillator by means of the homotopy perturbation method
Articles > Article · 2010
Authors: Ahmet YILDIRIM, Shaher MOMANI
International Journal of Computer Mathematics, Journal Indexed in SCI Expanded, International, WoS, 2010, vol 87, pp 1072-1082
DOI: 10.1080/00207160903082389
Summary
In this paper, we present a framework to obtain analytical solutions to a fractional oscillator by the homotopy perturbation method. The equation of motion of a driven fractional oscillator is obtained from the corresponding equation of motion of a driven harmonic oscillator by replacing the second-order time derivative by a fractional derivative of order α with 0<α≤2. The fractional derivative is described in the Caputo sense. Some examples are tested, and the results reveal that the technique introduced here is very effective and convenient for solving a fractional oscillator. The response characteristics of the fractional oscillator are studied for several cases.