A distributed‐order fractional diffusion equation with a singular density function: Analysis and approximation

Abstract

We prove the well-posedness and smoothing properties of a distributed-order time-fractional diffusion equation with a singular density function in multiple space dimensions, which could model the ultraslow subdiffusion processes. We accordingly derive a finite element approximation to the problem and prove its optimal-order error estimate. Numerical results are presented to support the mathematical and numerical analysis.