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Discrete Models of Time-Fractional Diffusion in a Potential Well

Gorenflo, R.Abdel-Rehim, E. — 2005

Fractional Calculus and Applied Analysis

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...

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