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Comb Model with Slow and Ultraslow Diffusion

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)18-33
Number of pages16
JournalMathematical Modelling of Natural Phenomena
Issue number3
Publication statusPublished - 2016
Publication typeA1 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.

ASJC Scopus subject areas


  • Anomalous diffusion, Comb-like model, Mean squared displacement, Probability density function

Publication forum classification

Field of science, Statistics Finland