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.
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