Comb Model with Slow and Ultraslow Diffusion
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||16|
|Journal||Mathematical Modelling of Natural Phenomena|
|Publication status||Published - 2016|
|Publication type||A1 Journal article-refereed|
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.