Subdiffusion with particle immobilization process described by 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. We propose the 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.