Cattaneo--type subdiffusion--reaction equation

Abstract

Subdiffusion in a system in which mobile particles $A$ can chemically react with static particles $B$ according to the rule $A+B\to B$ 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.

submitted to Phys. Rev. E

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Cited by in corpus (7)

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• Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
• Integral decomposition for the solutions of the generalized Cattaneo equation
• Model of anomalous diffusion--absorption process in a system consisting of two different media separated by a thin membrane
• Subdiffusion--absorption process in a system consisting of two different media
• Boundary conditions at a thin membrane that generate non--Markovian normal diffusion