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Velocity and displacement correlation functions for fractional generalized Langevin equations

  • We study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.

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Metadaten
Author:Trifce Sandev, Ralf MetzlerORCiDGND, Zivorad Tomovski
DOI:https://doi.org/10.2478/s13540-012-0031-2
ISSN:1311-0454 (print)
Parent Title (English):Fractional calculus and applied analysis : an international journal for theory and applications
Publisher:Versita
Place of publication:Warsaw
Document Type:Article
Language:English
Year of first Publication:2012
Year of Completion:2012
Release Date:2017/03/26
Tag:anomalous diffusion; fractional generalized Langevin equation; frictional memory kernel; mean square displacement; variances
Volume:15
Issue:3
Pagenumber:25
First Page:426
Last Page:450
Funder:Ministry of Education and Science of the Republic of Macedonia; NWO
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert