Electron. J. Differential Equations, Vol. 2019 (2019), No. 93, pp. 1-21.

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

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.

Show me the PDF file (357 KB), TEX file for this article.

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

Return to the EJDE web page