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Title: Fractional diffusion on bounded domains

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:
OSTI Identifier:
1183102
Report Number(s):
SAND--2014-17064J
Journal ID: ISSN 1311-0454; 537034
Grant/Contract Number:
AC04-94AL85000
Type:
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
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING fractional diffusion; boundary value problem; nonlocal diffusion; well-posed equation