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Title: Fractional diffusion on bounded domains

Abstract

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

Authors:
 [1];  [2];  [3];  [4];  [2];  [5]
  1. Michigan State Univ., East Lansing, MI (United States); Cankaya Univ., Ankara (Turkey)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  3. Columbia Univ., New York, NY (United States); Pennsylvania State Univ., State College, PA (United States)
  4. Florida State Univ., Tallahassee, FL (United States)
  5. Michigan State Univ., East Lansing, MI (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1183102
Report Number(s):
SAND-2014-17064J
Journal ID: ISSN 1311-0454; 537034
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Fractional Calculus and Applied Analysis
Additional Journal Information:
Journal Volume: 18; Journal Issue: 2; Journal ID: ISSN 1311-0454
Publisher:
de Gruyter
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; fractional diffusion; boundary value problem; nonlocal diffusion; well-posed equation

Citation Formats

Defterli, Ozlem, D'Elia, Marta, Du, Qiang, Gunzburger, Max Donald, Lehoucq, Richard B., and Meerschaert, Mark M. Fractional diffusion on bounded domains. United States: N. p., 2015. Web. doi:10.1515/fca-2015-0023.
Defterli, Ozlem, D'Elia, Marta, Du, Qiang, Gunzburger, Max Donald, Lehoucq, Richard B., & Meerschaert, Mark M. Fractional diffusion on bounded domains. United States. doi:10.1515/fca-2015-0023.
Defterli, Ozlem, D'Elia, Marta, Du, Qiang, Gunzburger, Max Donald, Lehoucq, Richard B., and Meerschaert, Mark M. Fri . "Fractional diffusion on bounded domains". United States. doi:10.1515/fca-2015-0023. https://www.osti.gov/servlets/purl/1183102.
@article{osti_1183102,
title = {Fractional diffusion on bounded domains},
author = {Defterli, Ozlem and D'Elia, Marta and Du, Qiang and Gunzburger, Max Donald and Lehoucq, Richard B. and Meerschaert, Mark M.},
abstractNote = {We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.},
doi = {10.1515/fca-2015-0023},
journal = {Fractional Calculus and Applied Analysis},
number = 2,
volume = 18,
place = {United States},
year = {Fri Mar 13 00:00:00 EDT 2015},
month = {Fri Mar 13 00:00:00 EDT 2015}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 21 works
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