Strong analytic solutions of fractional Cauchy problems
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- by Jebessa B. Mijena and Erkan Nane PDF
- Proc. Amer. Math. Soc. 142 (2014), 1717-1731 Request permission
Abstract:
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases a distributed order derivative can be used to model ultra-slow diffusion. We extend the results of Baeumer and Meerschaert in the single order fractional derivative case to the distributed order fractional derivative case. In particular, we develop strong analytic solutions of distributed order fractional Cauchy problems.References
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Additional Information
- Jebessa B. Mijena
- Affiliation: Department of Mathematics and Statistics, 221 Parker Hall, Auburn University, Auburn, Alabama 36849
- Address at time of publication: Department of Mathematics, Georgia College and State University, 231 W. Hancock Street, Campus Box 17, Milledgeville, Georgia 31061
- Email: jebessa.mijena@gcsu.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
- Received by editor(s): October 18, 2011
- Received by editor(s) in revised form: June 22, 2012
- Published electronically: February 19, 2014
- Communicated by: Mark M. Meerschaert
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 1717-1731
- MSC (2010): Primary 35R11, 35C15, 35S05; Secondary 47G30, 60K99
- DOI: https://doi.org/10.1090/S0002-9939-2014-11905-8
- MathSciNet review: 3168478