Revisiting the derivation of the fractional diffusion equation

Enrico Scalas; Rudolf Gorenflo; Francesco Mainardi; Marco Raberto

doi:10.1142/S0218348X0300194X

Revisiting the derivation of the fractional diffusion equation

Enrico Scalas
, Rudolf Gorenflo
, Francesco Mainardi
, Marco Raberto

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	281-289
Number of pages	9
Journal	Fractals
Volume	11
Issue number	SUPPL.
DOIs	https://doi.org/10.1142/S0218348X0300194X
Publication status	Published - Feb 2003
Externally published	Yes

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title = "Revisiting the derivation of the fractional diffusion equation",

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.",

author = "Enrico Scalas and Rudolf Gorenflo and Francesco Mainardi and Marco Raberto",

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AU - Mainardi, Francesco

AU - Raberto, Marco

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0037311921

U2 - 10.1142/S0218348X0300194X

DO - 10.1142/S0218348X0300194X

M3 - Article

SN - 0218-348X

VL - 11

SP - 281

EP - 289

JO - Fractals

JF - Fractals

IS - SUPPL.

ER -

Revisiting the derivation of the fractional diffusion equation

Abstract

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