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Strong analytic solutions of fractional Cauchy problems


Authors: Jebessa B. Mijena and Erkan Nane
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
Published electronically: February 19, 2014
MathSciNet review: 3168478
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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.


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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
Email: nane@auburn.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11905-8
Keywords: Distributed order Cauchy problems, Caputo fractional derivative, Riemann-Liouville fractional derivative, strongly analytic solution
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.