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 show...

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Bibliographic Details
Published in:Electronic journal of differential equations 2019-07, Vol.2019 (93), p.1-21
Main Authors: Lueling Jia, Huanzhen Chen, Vincent J. Ervin
Format: Article
Language:English
Subjects:
existence
Fractional diffusion equation
regularity
spectral method
Online Access:Get full text
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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