Crossover dynamics from superdiffusion to subdiffusion
- The Cattaneo or telegrapher's equation describes the crossover from initial ballistic to normal diffusion. Here we study and survey time-fractional generalisations of this equation that are shown to produce the crossover of the mean squared displacement from superdiffusion to subdiffusion. Conditional solutions are derived in terms of Fox H-functions and the dth-order moments as well as the diffusive flux of the different models are derived. Moreover, the concept of the distribution-like is proposed as an alternative to the probability density function.
Author details: | Emad AwadORCiD, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1515/fca-2020-0003 |
ISSN: | 1311-0454 |
ISSN: | 1314-2224 |
Title of parent work (English): | Fractional calculus and applied analysis : an international journal for theory and applications |
Subtitle (English): | models and solutions |
Publisher: | De Gruyter |
Place of publishing: | Berlin ; Boston |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/02/27 |
Publication year: | 2020 |
Release date: | 2023/05/23 |
Tag: | Cattaneo equation; Fox H-functions; anomalous diffusion; crossover dynamics; fractional dynamic equations; subdiffusion; superdiffusion and; telegrapher's equation |
Volume: | 23 |
Issue: | 1 |
Number of pages: | 48 |
First page: | 55 |
Last Page: | 102 |
Funding institution: | Alexander von Humboldt Polish Honorary Research Scholarship from the; Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej) |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access / Bronze Open-Access |