Existence and regularity of solutions to 1-D fractional order diffusion equations

Existence and regularity of solutions to 1-D fractional order diffusion equations

In this article we investigate the existence and regularity of 1-D steady state fractional order diffusion equations. Two models are investigated: the Riemann-Liouville fractional diffusion equation, and the Riemann-Liouville-Caputo fractional diffusion equation. For these models we explicitly s...

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Bibliographic Details
Main Authors: Lueling Jia, Huanzhen Chen, Vincent J. Ervin
Format: Article
Language:English
Published: Texas State University 2019-07-01
Series:Electronic Journal of Differential Equations
Subjects:
Fractional diffusion equation
existence
regularity
spectral method
Online Access:http://ejde.math.txstate.edu/Volumes/2019/93/abstr.html
Description
Summary:In this article we investigate the existence and regularity of 1-D steady state fractional order diffusion equations. Two models are investigated: the Riemann-Liouville fractional diffusion equation, and the Riemann-Liouville-Caputo fractional diffusion equation. For these models we explicitly show how the regularity of the solution depends upon the right hand side function. We also establish for which Dirichlet and Neumann boundary conditions the models are well posed.
ISSN:1072-6691

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