Lueling Jia, Huanzhen Chen, Vincent J. Ervin
Abstract:
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 Beijing, China email: lljia@csrc.ac.cn |
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Huanzhen Chen School of Mathematics and Statistics Shandong Normal University Jinan, China email: chhzh@sdnu.edu.cn |
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Vincent J. Ervin Department of Mathematical Sciences Clemson University Clemson, SC 29634-0975, USA email: vjervin@clemson.edu |
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