Fractional oscillator

TL;DR

This paper explores the fractional oscillator as a generalization of the linear oscillator using fractional calculus, interpreting it as an ensemble of harmonic oscillators with stochastic timing, revealing insights into dispersion and absorption.

Contribution

It introduces a novel interpretation of the fractional oscillator as an ensemble of harmonic oscillators with slightly different frequencies, linking fractional calculus to dispersion analysis.

Findings

Intrinsic absorption arises from ensemble averaging of oscillators.

Dispersion characteristics are analogous to media described by fractional oscillators.

The analysis highlights the role of frequency variation among oscillators.

Abstract

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.