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


YILDIRIM A. , MOMANI S.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.87, ss.1072-1082, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 87 Konu: 5
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1080/00207160903082389
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Sayfa Sayıları: ss.1072-1082

Özet

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 alpha with 0 < a <= 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.