TY  - JOUR
A1  - Sandev, Trifce
A1  - Chechkin, Aleksei V.
A1  - Korabel, Nickolay
A1  - Kantz, Holger
A1  - Sokolov, Igor M.
A1  - Metzler, Ralf
T1  - Distributed-order diffusion equations and multifractality: Models and solutions
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - 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.
Y1  - 2015
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/38517
SN  - 1539-3755
SN  - 1550-2376
VL  - 92
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  -