Dynamics of the fractional oscillator

The integral equation of motion of a simple harmonic oscillator is generali zed by taking the integral to be of arbitrary order according to the method s of fractional calculus to yield the equation of motion of a fractional os cillator. The solution is obtained in terms of Mittag-Leffler functions usi ng Laplace transforms. The expressions for the generalized momentum and the total energy of the fractional oscillator are also obtained. Numerical app lication and the phase plane representation of the dynamics are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.