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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Transient anomalous sub-diffusion on bounded domains
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by Mark M. Meerschaert, Erkan Nane and P. Vellaisamy PDF
Proc. Amer. Math. Soc. 141 (2013), 699-710 Request permission

Abstract:

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables and eigenfunction expansions in time and space are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.
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Additional Information
  • Mark M. Meerschaert
  • Affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48823
  • Email: mcubed@stt.msu.edu
  • Erkan Nane
  • Affiliation: Department of Mathematics and Statistics, 221 Parker Hall, Auburn University, Auburn, Alabama 36849
  • MR Author ID: 782700
  • Email: nane@auburn.edu
  • P. Vellaisamy
  • Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
  • Email: pv@math.iit.ac.in
  • Received by editor(s): May 2, 2011
  • Received by editor(s) in revised form: July 8, 2011
  • Published electronically: June 26, 2012
  • Additional Notes: The first author was partially supported by NSF grants DMS-1025486, DMS-0803360, EAR-0823965 and NIH grant R01-EB012079-01.
    This paper was completed while the third author was visiting Michigan State University.
  • Communicated by: Edward C. Waymire
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 699-710
  • MSC (2010): Primary 60G52, 35Q86; Secondary 35P10
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11362-0
  • MathSciNet review: 2996975