Subdiffusion with particle immobilization process described by a differential equation with Riemann-Liouville-type fractional time derivative.

Abstract

An equation describing subdiffusion with possible immobilization of particles is derived by means of the continuous time random walk model. The equation contains a fractional time derivative of Riemann-Liouville type which is a differential-integral operator with the kernel defined by the Laplace transform; the kernel controls the immobilization process. We propose a method for calculating the inverse Laplace transform providing the kernel in the time domain. In the long time limit the subdiffusion-immobilization process reaches a stationary state in which the probability density of a particle distribution is an exponential function.