Reaction-subdiffusion equations

To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion A -> 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.