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Title: Fractional diffusion on bounded domains

Journal Article · · Fractional Calculus and Applied Analysis
 [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)
+ Show Author Affiliations

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.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1183102
Report Number(s):
SAND-2014-17064J; 537034
Journal Information:
Fractional Calculus and Applied Analysis, Vol. 18, Issue 2; ISSN 1311-0454
Publisher:
de GruyterCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 70 works
Citation information provided by
Web of Science

References (5)

Generalized Fick’s Law and Fractional ADE for Pollution Transport in a River: Detailed Derivation journal January 2006
A novel numerical method for the time variable fractional order mobile–immobile advection–dispersion model journal September 2013
The fractional-order governing equation of Lévy Motion journal February 2000
Application of a fractional advection-dispersion equation journal February 2000
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints journal January 2012

Cited By (11)

Space‐time fractional Dirichlet problems journal August 2018
Galerkin‐Legendre spectral method for the nonlinear Ginzburg‐Landau equation with the Riesz fractional derivative journal September 2019
Finite difference scheme for time‐space fractional diffusion equation with fractional boundary conditions journal December 2019
Variational formulation and efficient implementation for solving the tempered fractional problems journal February 2018
An efficient difference scheme for the coupled nonlinear fractional Ginzburg–Landau equations with the fractional Laplacian journal September 2018
A second‐order finite difference method for fractional diffusion equation with Dirichlet and fractional boundary conditions journal January 2019
Determine a Space-Dependent Source Term in a Time Fractional Diffusion-Wave Equation journal March 2019
Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction–Diffusion Equation journal August 2018
Time and Space Fractional Diffusion in Finite Systems journal March 2018
Identifying the Fractional Orders in Anomalous Diffusion Models from Real Data journal February 2018
Variational formulation and efficient implementation for solving the tempered fractional problems text January 2016

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Related Subjects

97 MATHEMATICS AND COMPUTING
fractional diffusion
boundary value problem
nonlocal diffusion
well-posed equation