To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion $A\to B$. We derive the corresponding kinetic equations for the local $A$ and $B$ concentrations. Their form is rather unusual: The parameters of the reaction influence the diffusion term in the equation for a component $A$, a consequence of the non-Markovian nature of subdiffusion. The equation for the product contains a term which depends on the concentration of $A$ at all previous times. Our discussion shows that reaction-subdiffusion equations may not resemble the corresponding reaction-diffusion ones and are not obtained by a trivial change of the diffusion operator for a subdiffusion one.

• Received 12 October 2005

DOI:https://doi.org/10.1103/PhysRevE.73.031102