From continuous time random walks to the generalized diffusion equation-Reference-Cited by-同舟云学术

From continuous time random walks to the generalized diffusion equation

Published:2018-02-01 Issue:1 Volume:21 Page:10-28
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Sandev Trifce¹²³,Metzler Ralf⁴,Chechkin Aleksei⁴⁵

Affiliation:

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 in Skopje , P.O. Box 162, 1001 , 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. Institute for Physics and Astronomy , Karl-Liebknecht-St. 24/25 , University of Potsdam , D-14776 , Potsdam-Golm , Germany

5. Akhiezer Institute for Theoretical Physics , Akademicheskaya St. 1 , Kharkov , 61108 , Ukraine

Abstract

Abstract We obtain a generalized diffusion equation in modified or Riemann-Liouville form from continuous time random walk theory. The waiting time probability density function and mean squared displacement for different forms of the equation are explicitly calculated. We show examples of generalized diffusion equations in normal or Caputo form that encode the same probability distribution functions as those obtained from the generalized diffusion equation in modified form. The obtained equations are general and many known fractional diffusion equations are included as special cases.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2018-0002/pdf

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