Fractional oscillator
  We consider the fractional oscillator being 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 stochastic time arrow. The intrinsic absorption of the fractional oscillator results from the full contribution of the harmonic oscillators' ensemble: these oscillators differs a little from each other in frequency so that each response is compensated by an antiphase response of another harmonic oscillator. This allows to draw a parallel in the dispersion analysis for the media described by the fractional oscillator and the ensemble of ordinary harmonic oscillators with damping. The features of this analysis are discussed. 
Aleksander Stanislavsky
cond-mat.stat-mech