TY  - JOUR
A1  - Sandev, Trifce
A1  - Sokolov, Igor M.
A1  - Metzler, Ralf
A1  - Chechkin, Aleksei V.
T1  - Beyond monofractional kinetics
JF  - Chaos, solitons & fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science
N2  - We discuss generalized integro-differential diffusion equations whose integral kernels are not of a simple power law form, and thus these equations themselves do not belong to the family of fractional diffusion equations exhibiting a monoscaling behavior. They instead generate a broad class of anomalous nonscaling patterns, which correspond either to crossovers between different power laws, or to a non-power-law behavior as exemplified by the logarithmic growth of the width of the distribution. We consider normal and modified forms of these generalized diffusion equations and provide a brief discussion of three generic types of integral kernels for each form, namely, distributed order, truncated power law and truncated distributed order kernels. For each of the cases considered we prove the non-negativity of the solution of the corresponding generalized diffusion equation and calculate the mean squared displacement. (C) 2017 Elsevier Ltd. All rights reserved.
KW  - Distributed order diffusion-wave equations
KW  - Complete Bernstein function
KW  - Completely monotone function
Y1  - 2017
U6  - https://doi.org/10.1016/j.chaos.2017.05.001
SN  - 0960-0779
SN  - 1873-2887
VL  - 102
SP  - 210
EP  - 217
PB  - Elsevier
CY  - Oxford
ER  -