An introduction to fractional diffusion

Paper

Henry, B. I., Langlands, Trevor and Straka, P.. 2010. "An introduction to fractional diffusion." Dewar, Robert L. and Detering, Frank (ed.) 22nd Canberra International Physics Summer School. Canberra, Australia 08 - 19 Dec 2008 Singapore. https://doi.org/10.1142/9789814277327_0002
Paper/Presentation Title

An introduction to fractional diffusion

Presentation TypePaper
AuthorsHenry, B. I. (Author), Langlands, Trevor (Author) and Straka, P. (Author)
EditorsDewar, Robert L. and Detering, Frank
Journal or Proceedings TitleComplex Physical, Biophysical and Econophysical Systems
Journal Citation9, pp. 37-89
Number of Pages43
Year2010
Place of PublicationSingapore
ISBN9789814277327
Digital Object Identifier (DOI)https://doi.org/10.1142/9789814277327_0002
Web Address (URL) of Paperhttp://site.ebrary.com/lib/unisouthernqld/Doc?id= 1 0422486&ppg=48
Conference/Event22nd Canberra International Physics Summer School
Event Details
22nd Canberra International Physics Summer School
Event Date
08 to end of 19 Dec 2008
Event Location
Canberra, Australia
Abstract

The mathematical description of diffusion has a long history with many different formulations including phenomenological models based on conservation of mass and constitutive laws; probabilistic models based on random walks and central limit theorems; microscopic stochastic models based on Brownian motion and Langevin equations; and mesoscopic stochastic models based on master equations and Fokker-Planck equations. A fundamental result common to the different approaches is that the mean square displacement of a diffusing particle scales linearly with time. However there have been numerous experimental measurements in which the mean square displacement of diffusing particles scales as a fractional order power law in time. In recent years a great deal of progress has been made in extending the different models for diffusion to incorporate this fractional diffusion. The tools of fractional calculus have proven very useful in these developments, linking together fractional constitutive laws, continuous time random walks, fractional Langevin equations and fractional Brownian motions. These notes provide a tutorial style overview of standard and fractional diffusion processes.

Keywordsfractional calculus; anomalous subdiffusion; random walks; superdiffusion
ANZSRC Field of Research 2020490510. Stochastic analysis and modelling
519901. Complex physical systems
490410. Partial differential equations
Public Notes

Chapter 2. Electronic copy held USQ Library
For more information contact Dr Trevor Langlands Trevor.Langlands@usq.edu.au

Byline AffiliationsUniversity of New South Wales
SeriesWorld Scientfic Lecture Notes in Complex Systems
Book TitleComplex Physical, Biophysical and Econphysical Systems: Proceedings of the 22nd Canberra International Physics Summer School
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