IJPAM: Volume 37, No. 1 (2007)

ANALYTICAL SOLUTIONS OF A FRACTIONAL
OSCILLATOR BY THE DECOMPOSITION METHOD

Shaher Momani$^1$, Rabha W. Ibrahim$^2$
$^1$Department of Mathematics
Faculty of Arts and Sciences
Qatar University
P.O. Box 2317, Doha, QATAR
e-mail: shahermm@yahoo.com
$^2$P.O. Box 14526, Maeen Sana'a, YEMEN
e-mail: rabhaibrahim@yahoo.com


Abstract.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 $1<\alpha \leq 2$. The fractional derivative is described in the Caputo sense. The application of Adomian decomposition method, developed for differential equations of integer order, is extended to derive analytical solutions of the fractional oscillator. The response characteristics and phase plane representation of the fractional oscillator are studied for several cases.

Received: April 2, 2007

AMS Subject Classification: 26A33

Key Words and Phrases: fractional oscillator, Caputo fractional derivative, decomposition method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 1