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 |
|---|---|
| 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 |
