Notes on Convergence Results for Parabolic Equations with Riemann–Liouville Derivatives

Abstract

Fractional diffusion equations have applications in various fields and in this paper we consider a fractional diffusion equation with a Riemann–Liouville derivative. The main objective is to investigate the convergence of solutions of the problem when the fractional order tends to 1−. Under some suitable conditions on the Cauchy data, we prove the convergence results in a reasonable sense.

Keywords

• fractional diffusion equation
• Riemman–Liouville
• regularity
• convergence rate