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.
| 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 |
