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We propose a reaction-transport model for CTRW with non-linear reactions andnon-exponential waiting time distributions. We derive non-linear evolutionequation for mesoscopic density of particles. We apply this equation to theproblem of fronts propagation into unstable state of reaction-transport systemswith anomalous diffusion. We have found an explicit expression for the speed ofpropagating front in the case of subdiffusion transport.

Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts