Authors
Ralf Metzler, Joseph Klafter
Publication date
2000/4/1
Journal
Physica A: Statistical Mechanics and its Applications
Volume
278
Issue
1-2
Pages
107-125
Publisher
North-Holland
Description
The fractional diffusion equation is solved for different boundary value problems, these being absorbing and reflecting boundaries in half-space and in a box. Thereby, the method of images and the Fourier–Laplace transformation technique are employed. The separation of variables is studied for a fractional diffusion equation with a potential term, describing a generalisation of an escape problem through a fluctuating bottleneck. The results lead to a further understanding of the fractional framework in the description of complex systems which exhibit anomalous diffusion.
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R Metzler, J Klafter - Physica A: Statistical Mechanics and its Applications, 2000