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Revisiting the derivation of the fractional diffusion equation

Enrico Scalas·Rudolf Gorenflo·Francesco Mainardi·Marco Raberto
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Abstract

The fractional diffusion equation is derived from the master equation of continuous-time random walks (CTRWs) via a straightforward application of the Gnedenko-Kolmogorov limit theorem. The Cauchy problem for the fractional diffusion equation is solved in various important and general cases. The meaning of the proper diffusion limit for CTRWs is discussed.

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Enrico Scalas, Rudolf Gorenflo, Francesco Mainardi, Marco Raberto. 2002-10-11. Revisiting the derivation of the fractional diffusion equation. https://doi.org/10.1142/9789812778109_0029

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