TY  - JOUR
A1  - Sandev, T.
A1  - Iomin, Alexander
A1  - Kantz, Holger
A1  - Metzler, Ralf
A1  - Chechkin, Aleksei V.
T1  - Comb Model with Slow and Ultraslow Diffusion
JF  - Mathematical modelling of natural phenomena
N2  - We consider a generalized diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyze the probability distribution functions and we derive the mean squared displacement in x and y directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both x and y directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We give the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process.
KW  - comb-like model
KW  - anomalous diffusion
KW  - mean squared displacement
KW  - probability density function
Y1  - 2016
U6  - https://doi.org/10.1051/mmnp/201611302
SN  - 0973-5348
SN  - 1760-6101
VL  - 11
SP  - 18
EP  - 33
PB  - EDP Sciences
CY  - Les Ulis
ER  -