title: Distributed-order diffusion equations and multifractality: Models and solutions.
abstract: 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.
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.|Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia.
authors.forename: Trifce
authors.initials: T
authors.lastname: Sandev
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.|Akhiezer Institute for Theoretical Physics, Kharkov 61108, Ukraine.|Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany.
authors.forename: Aleksei V
authors.initials: AV
authors.lastname: Chechkin
authors.affiliation: School of Mathematics, The University of Manchester, Manchester M60 1QD, United Kingdom.
authors.forename: Nickolay
authors.initials: N
authors.lastname: Korabel
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
authors.forename: Holger
authors.initials: H
authors.lastname: Kantz
authors.affiliation: Institute of Physics, Humboldt University Berlin, Newtonstrasse 15, D-12489 Berlin, Germany.
authors.forename: Igor M
authors.initials: IM
authors.lastname: Sokolov
authors.affiliation: Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany.|Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.
authors.forename: Ralf
authors.initials: R
authors.lastname: Metzler