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Zbl 1189.35355
Chen, Wen; Sun, Hongguang; Zhang, Xiaodi; Korošak, Dean
Anomalous diffusion modeling by fractal and fractional derivatives. (English)
[J] Comput. Math. Appl. 59, No. 5, 1754-1758 (2010). ISSN 0898-1221

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 2000:: *35R11
26A33 Fractional derivatives and integrals (real functions)
35A08 Fundamental solutions of PDE

Keywords: heavy tail; anomalous diffusion; fractal derivative; fractional derivative; power law

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