Crossover dynamics from superdiffusion to subdiffusion: Models and solutions-Reference-Cited by-同舟云学术

Crossover dynamics from superdiffusion to subdiffusion: Models and solutions

Published:2020-02-01 Issue:1 Volume:23 Page:55-102
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Awad Emad¹,Metzler Ralf²

Affiliation:

1. Department of Mathematics , Faculty of Education Alexandria University , Souter St., El-Shatby, P.O. Box 21526 , Alexandria , Egypt

2. Institute of Physics & Astronomy , University of Potsdam , Karl-Liebknecht-Str. 24/25 D-14476 , Potsdam-Golm , Germany

Abstract

Abstract The Cattaneo or telegrapher’s equation describes the crossover from initial ballistic to normal diffusion. Here we study and survey time-fractional generalisations of this equation that are shown to produce the crossover of the mean squared displacement from superdiffusion to subdiffusion. Conditional solutions are derived in terms of Fox H-functions and the δth-order moments as well as the diffusive flux of the different models are derived. Moreover, the concept of the distribution-like is proposed as an alternative to the probability density function.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0003/pdf

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