Distributed-order diffusion equations and multifractality: Models and solutions
- We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Author details: | Trifce SandevORCiDGND, Aleksei ChechkinORCiDGND, Nickolay Korabel, Holger KantzORCiD, Igor M. SokolovORCiDGND, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1103/PhysRevE.92.042117 |
ISSN: | 1539-3755 |
ISSN: | 1550-2376 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/26565178 |
Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
Publisher: | American Physical Society |
Place of publishing: | College Park |
Publication type: | Article |
Language: | English |
Year of first publication: | 2015 |
Publication year: | 2015 |
Release date: | 2017/03/27 |
Volume: | 92 |
Issue: | 4 |
Number of pages: | 19 |
Funding institution: | IMU Berlin Einstein Foundation; Academy of Finland (Suomen Akatemia) through the FiDiPro scheme |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |