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Anomalous diffusion modeling by fractal and fractional derivatives. (English) Zbl 1189.35355

Summary: This paper makes an attempt to develop a fractal derivative model of anomalous diffusion. We also derive the fundamental solution of the fractal derivative equation for anomalous diffusion, which characterizes a clear power law. This new model is compared with the corresponding fractional derivative model in terms of computational efficiency, diffusion velocity, and heavy tail property. The merits and distinctions of these two models of anomalous diffusion are then summarized.

MSC:

35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
35A08 Fundamental solutions to PDEs
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