Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 93, pp. 1-21.

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

Authors: Lueling Jia (Beijing Computational Science Research Center, China)
         Huanzhen Chen (Shandong Normal Univ., Jinan, China)
         Vincent J. Ervin (Clemson Univ., Clemson, SC, USA)
 
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.