2004/11/15 by A. A. Stanislavsky, Aleksander Stanislavsky · 4 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Mechanical and Optical Resonators #Probabilistic and Robust Engineering Design #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.70.051103
published as Phys. Rev. E 70, 051103 (2004) · 6 pages, 3 figures
openalex publication_date 2004/11/15 · arxiv created 2011/11/13 · arxiv updated 2011/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.