Regularity of the solution to 1-D fractional order diffusion equations
Vincent J. Ervin, Norbert Heuer and John Paul Roop
Math. Comp. 87 (313), 2273-2294, 2018.
In this article we investigate the solution of the steady-state fractional diffusion equation on
a bounded domain in R1. From an analysis of the underlying model problem, we postulate
that the fractional diffusion operator in the modeling equations is neither the Riemann-Liouville
nor the Caputo fractional differential operators. We then find a closed form expression for the
kernel of the fractional diffusion operator which, in most cases, determines the regularity of
the solution. Next we establish that the Jacobi polynomials are pseudo eigenfunctions for the
fractional diffusion operator. A spectral type approximation method for the solution of the
steady-state fractional diffusion equation is then proposed and studied.