TY - JOUR
T1 - Boundary value problems for fractional diffusion equations
AU - Metzler, Ralf
AU - Klafter, Joseph
N1 - Funding Information:
RM is supported in part through an Amos de Shalit fellowship from MINERVA, and through a Feodor-Lynen fellowship from the Alexander von Humboldt Stiftung, Bonn am Rhein, Germany. Financial assistance from GIF and the TMR programme of the European Commission is acknowledged as well. RM thanks Norbert Südland for help with Mathematica, and Israela Becker for helpful comments.
PY - 2000/4/1
Y1 - 2000/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0033884660&partnerID=8YFLogxK
U2 - 10.1016/S0378-4371(99)00503-8
DO - 10.1016/S0378-4371(99)00503-8
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AN - SCOPUS:0033884660
SN - 0378-4371
VL - 278
SP - 107
EP - 125
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1
ER -