Discrete Models of Time-Fractional Diffusion in a Potential Well

Gorenflo, R.; Abdel-Rehim, E.

Fractional Calculus and Applied Analysis (2005)

  • Volume: 8, Issue: 2, page 173-200
  • ISSN: 1311-0454

Abstract

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Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity are discussed, and results of numerical case studies are displayed. See also, http://www.diss.fu-berlin.de/2004/168/index.html

How to cite

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Gorenflo, R., and Abdel-Rehim, E.. "Discrete Models of Time-Fractional Diffusion in a Potential Well." Fractional Calculus and Applied Analysis 8.2 (2005): 173-200. <http://eudml.org/doc/11287>.

@article{Gorenflo2005,
abstract = {Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity are discussed, and results of numerical case studies are displayed. See also, http://www.diss.fu-berlin.de/2004/168/index.html},
author = {Gorenflo, R., Abdel-Rehim, E.},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 45K05; 60J60; 60G50; 65N06},
language = {eng},
number = {2},
pages = {173-200},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Discrete Models of Time-Fractional Diffusion in a Potential Well},
url = {http://eudml.org/doc/11287},
volume = {8},
year = {2005},
}

TY - JOUR
AU - Gorenflo, R.
AU - Abdel-Rehim, E.
TI - Discrete Models of Time-Fractional Diffusion in a Potential Well
JO - Fractional Calculus and Applied Analysis
PY - 2005
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 8
IS - 2
SP - 173
EP - 200
AB - Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity are discussed, and results of numerical case studies are displayed. See also, http://www.diss.fu-berlin.de/2004/168/index.html
LA - eng
KW - 26A33; 45K05; 60J60; 60G50; 65N06
UR - http://eudml.org/doc/11287
ER -

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