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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.

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Author:Trifce Sandev, Aleksei V. ChechkinORCiDGND, Nickolay Korabel, Holger Kantz, Igor M. Sokolov, Ralf MetzlerORCiDGND
ISSN:1539-3755 (print)
ISSN:1550-2376 (online)
Pubmed Id:
Parent Title (English):Physical review : E, Statistical, nonlinear and soft matter physics
Publisher:American Physical Society
Place of publication:College Park
Document Type:Article
Year of first Publication:2015
Year of Completion:2015
Release Date:2017/03/27
Funder: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