Reaction-subdiffusion on moving fluids

To capture the dynamic behaviors of reaction-subdiffusion in flow fields, in the present paper we analyze a simple monomolecular conversion A $\to$ B. We derive the corresponding master equations for the distribution of A and B particles in continuous time random walks scheme. The new results are then used to obtain the generalizations of advection-diffusion reaction equation, in which the diffusion and advection operators both depend on the reaction rate.