Model of subdiffusion--absorption process in a membrane system consisting of two different media

TL;DR

This paper develops a mathematical model for subdiffusion and absorption in a two-media membrane system, deriving Green's functions and boundary conditions using fractional calculus and random walk methods.

Contribution

It introduces a novel approach to derive Green's functions and boundary conditions for subdiffusion-absorption in membrane systems with fractional derivatives.

Findings

Derived Green's functions for the system

Established boundary conditions at the membrane

Presented a method linking discrete random walks to continuous models

Abstract

We consider the subdiffusion--absorption process in a system which consists of two different media separated by a thin membrane. The process is described by subdiffusion--absorption equations with fractional Riemann--Liouville time derivative. We present the method of deriving the probabilities (the Green's functions) described particle's random walk in the system. Within the method we firstly consider the random walk of a particle in a system with both discrete time and space variables, and then we pass from discrete to continuous variables by means of the procedure presented in this paper. Using the Green's functions we derive boundary conditions at the membrane.