Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 278, Issue 1-2, Pages 107-125Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/S0378-4371(99)00503-8
Keywords
fractional diffusion equation; boundary value problems; Mittag-Leffler relaxation; anomalous diffusion; anomalous relaxation
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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 Fouker-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. (C) 2000 Elsevier Science B.V. All rights reserved.
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