We consider a fractional oscillator which is a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by a stochastic time arrow. The intrinsic absorption of the fractional oscillator results from the full contribution of the harmonic oscillator ensemble: these oscillators differ a little from each other in frequency so that each response is compensated by an antiphase response of another harmonic oscillator. This allows one to draw a parallel in the dispersion analysis for media described by a fractional oscillator and an ensemble of ordinary harmonic oscillators with damping. The features of this analysis are discussed.
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A. A. Stanislavsky (2004) studied this question.
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