  Understanding anomalous transport and reaction kinetics due to microscopic
physical and chemical disorder is a long-standing goal in many fields including
geophysics, biology, and engineering. We consider reaction-diffusion
characterized by fluctuations in both transitions times and decay rates. We
introduce and analyze a model framework that explicitly connects microscopic
fluctuations with the mescoscopic description. For broad distributions of
transport and reaction time scales we compute the particle density and derive
the equations governing its evolution, finding power-law decay of the survival
probability, and spatially heterogeneous decay that leads to subdiffusion and
an asymptotically stationary surviving-particle density. These anomalies are
clearly attributable to non-Markovian effects that couple transport and
chemical properties in both reaction and diffusion terms.
