Geodesic
Discrete Models of Time-Fractional Diffusion in a Potential Well
Fractional calculus and applied analysis, Tome 8 (2005) no. 2, pp. 173-200

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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
Keywords: Generalization of Ehrenfest’s urn Model, Diffusion Processes with Memory and Central Drift in a Potential Well, Difference Schemes, Random Walk Models, Fractional Derivative, Stochastic Processes, 26A33, 45K05, 60J60, 60G50, 65N06 
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Gorenflo, R.; Abdel-Rehim, E. Discrete Models of Time-Fractional Diffusion in a Potential Well. Fractional calculus and applied analysis, Tome 8 (2005) no. 2, pp. 173-200. http://geodesic.mathdoc.fr/item/FCAA_2005_8_2_a5/