Lueling Jia, Huanzhen Chen, Vincent J. Ervin
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.
Submitted September 24, 2018. Published July 26, 2019.
Math Subject Classifications: 35R11, 35R25, 65N35.
Key Words: Fractional diffusion equation; existence; regularity; spectral method.
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| Lueling Jia |
Applied and Computational Mathematics Division
Beijing Computational Science Research Center
| Huanzhen Chen |
School of Mathematics and Statistics
Shandong Normal University
| Vincent J. Ervin |
Department of Mathematical Sciences
Clemson, SC 29634-0975, USA
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