  A fractional reaction-diffusion equation is derived from a continuous time
random walk model when the transport is dispersive. The exit from the encounter
distance, which is described by the algebraic waiting time distribution of jump
motion, interferes with the reaction at the encounter distance. Therefore, the
reaction term has a memory effect. The derived equation is applied to the
geminate recombination problem. The recombination is shown to depend on the
intrinsic reaction rate, in contrast with the results of Sung et al. [J. Chem.
Phys. {\bf 116}, 2338 (2002)], which were obtained from the fractional
reaction-diffusion equation where the diffusion term has a memory effect but
the reaction term does not. The reactivity dependence of the recombination
probability is confirmed by numerical simulations.
