## 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.## References

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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