Subdiffusion with particle immobilization process described by differential equation with Riemann--Liouville type fractional time derivative
arXiv:2302.09679 · doi:10.1103/PhysRevE.108.014132
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.
arXiv comment5 pages, 3 figures
References in corpus (15)
- From Diffusion to Anomalous Diffusion: A Century after Einstein's Brownian Motion
- Reaction Front in an A+B -> C Reaction-Subdiffusion Process
- Nonergodic Subdiffusion from Brownian Motion in an Inhomogeneous Medium
- On reaction-subdiffusion equations
- Why the Mittag-Leffler function can be considered the Queen function of the Fractional Calculus?
- Diffusion and Relaxation Controlled by Tempered α-stable Processes
- How to Measure Subdiffusion Parameters
- Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts
- Continuous time random walk with correlated waiting times
- Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous time random walks
- From the solutions of diffusion equation to the solutions of subdiffusive one
- Diffusion of antibiotics through a biofilm in the presence of diffusion and absorption barriers
- Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
- A Tutorial on the Basic Special Functions of Fractional Calculus
- Subdiffusion--reaction process with reactions versus subdiffusion--reaction process with reactions