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On fractional diffusion and continuous time random walks

R. Hilfer
ICA-1, Universität Stuttgart, 70569 Stuttgart, Germany
Institut für Physik, Universität Mainz, 55099 Mainz, Germany
results presented at the INTAS’03 meeting, Kopenhagen, May 3rd, 2003

A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in general not asymptotically equivalent.

Key words and phrases:
fractional calculus, fractional diffusion, anomalous diffusion, subdiffusion, continuous time random walks, power law tail
PACS: 67.40.Pf, 77.22.-d, 78.30.Ly