From continuous time random walks to the generalized diffusion equation
- We obtain a generalized diffusion equation in modified or Riemann-Liouville form from continuous time random walk theory. The waiting time probability density function and mean squared displacement for different forms of the equation are explicitly calculated. We show examples of generalized diffusion equations in normal or Caputo form that encode the same probability distribution functions as those obtained from the generalized diffusion equation in modified form. The obtained equations are general and many known fractional diffusion equations are included as special cases.
| Author details: | Trifce SandevORCiD, Ralf MetzlerORCiDGND, Aleksei V. ChechkinORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1515/fca-2018-0002 |
| ISSN: | 1311-0454 |
| ISSN: | 1314-2224 |
| Title of parent work (English): | Fractional calculus and applied analysis : an international journal for theory and applications |
| Publisher: | De Gruyter |
| Place of publishing: | Berlin |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2018/03/23 |
| Publication year: | 2018 |
| Release date: | 2022/01/26 |
| Tag: | Mittag-Leffler functions; anomalous diffusion; continuous time random walk (CTRW); generalized diffusion equation |
| Volume: | 21 |
| Issue: | 1 |
| Number of pages: | 19 |
| First page: | 10 |
| Last Page: | 28 |
| Funding institution: | Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [ME 1535/6-1] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 52 Astronomie / 520 Astronomie und zugeordnete Wissenschaften |
| 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
| Peer review: | Referiert |
| Publishing method: | Open Access / Bronze Open-Access |
