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 transport 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 varying 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.
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