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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Space-time fractional derivative operators


Authors: Boris Baeumer, Mark M. Meerschaert and Jeff Mortensen
Journal: Proc. Amer. Math. Soc. 133 (2005), 2273-2282
MSC (2000): Primary 47G30; Secondary 60J60
Published electronically: March 14, 2005
MathSciNet review: 2138870
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Abstract: Evolution equations for anomalous diffusion employ fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. This paper develops the mathematical foundations of those operators.


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Additional Information

Boris Baeumer
Affiliation: Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand
Email: bbaeumer@maths.otago.ac.nz

Mark M. Meerschaert
Affiliation: Department of Physics, University of Nevada, Reno, Nevada 89557-0084
Address at time of publication: Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand
Email: mcubed@unr.edu, mcubed@maths.otago.ac.nz

Jeff Mortensen
Affiliation: Department of Mathematics, University of Nevada, Reno, Nevada 89557-0084
Email: jm@unr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07949-9
PII: S 0002-9939(05)07949-9
Keywords: Evolution equation, anomalous diffusion, fractional derivative
Received by editor(s): April 25, 2003
Published electronically: March 14, 2005
Additional Notes: The first author was partially supported by the Marsden fund, administered by the Royal Society of New Zealand
The second author was partially supported by NSF grants DMS-0139927 and DMS-0417869 as well as the Marsden fund, administered by the Royal Society of New Zealand
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society