Recombination kinetics in subdiffusive media

We study the kinetics of the recombination reaction in subdiffusive media, where the displacement of reactants r(t) follows ∝tα with 0<α<1. We derive a rigorous fractional reaction-diffusion equation from a continuous time random walk model and calculate the kinetics of recombination reaction on the basis of this equation. The survival probability of a particle starting at r0 has an asymptotic time dependence of t-α/2 for both the perfectly absorbing and the partially reflecting boundary conditions. The change in the boundary condition alters only the coefficient for the asymptotic time dependence. The asymptotic time dependence of the survival probability is confirmed by the numerical simulations and supported by the results of a lattice model