Cattaneo--type subdiffusion--reaction equation

TL;DR

This paper derives a Cattaneo-type subdiffusion-reaction equation incorporating chemical reactions between mobile and static particles using a persistent random walk model and fractional calculus, providing solutions for long-term behavior.

Contribution

It introduces a novel fractional subdiffusion-reaction equation based on a persistent random walk model, extending previous models to include complex chemical reactions.

Findings

Derived the Cattaneo--type subdiffusion--reaction equation with fractional derivatives.

Obtained solutions for the long-time behavior of the system.

Extended the model to more complex reaction rules.

Abstract

Subdiffusion in a system in which mobile particles $A$ can chemically react with static particles $B$ according to the rule $A+B\rightarrow B$ is considered within a persistent random walk model. This model, which assumes a correlation between successive steps of particles, provides hyperbolic Cattaneo normal diffusion or fractional subdiffusion equations for a system without chemical reactions. Starting with the difference equation, which describes a persistent random walk in a system with chemical reactions, using the generating function method and the continuous time random walk formalism, we will derive the Cattaneo--type subdiffusion differential equation with fractional time derivatives in which the chemical reactions mentioned above are taken into account. We will also find its solution over a long time limit. Based on the obtained results, we will find the Cattaneo--type subdiffusion--reaction equation in the case in which mobile particles of species $A$ and $B$ can chemically react according to a more complicated rule.