Volume 124, Number 2, October 2018
|Number of page(s)||7|
|Published online||19 November 2018|
Finite-velocity diffusion on a comb
1 Radiation Safety Directorate - Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia
2 Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss Cyril and Methodius University Arhimedova 3, 1000 Skopje, Macedonia
3 Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
4 Department of Physics, Technion - Haifa 32000, Israel
Received: 20 August 2018
Accepted: 18 October 2018
A Cattaneo equation for a comb structure is considered. We present a rigorous analysis of the obtained fractional diffusion equation, and corresponding solutions for the probability distribution function are obtained in the form of the Fox H-function and its infinite series. The mean square displacement along the backbone is obtained as well in terms of the infinite series of the Fox H-function. The obtained solutions describe the transition from normal diffusion to subdiffusion, which results from the comb geometry.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 87.19.L- – Neuroscience / 82.40.-g – Chemical kinetics and reactions: special regimes and techniques
© EPLA, 2018
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