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Section B Special Section: New Analytical Methods

Series solutions of a fractional oscillator by means of the homotopy perturbation method

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Pages 1072-1082 | Received 26 Dec 2008, Accepted 31 May 2009, Published online: 10 May 2010
 

Abstract

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.

2000 AMS Subject Classifications::

Acknowledgements

The authors are grateful to the referees for their invaluable suggestions and comments for the improvement of the paper.

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