Aging continuous time random walks with A → B reaction
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Aging continuous time random walk (ACTRW) which describes a dynamical process starting at time − ta before the first measurement at t = 0 attracts more and more attentions in recent years. To describe the aging behaviors of reactive particles in anomalous diffusion process in disordered medium, in this paper we introduce a new ACTRW model with simple A → B reaction, and obtain the corresponding generalized Montroll-Weiss equations in Fourier-Laplace space for the densities of A and B particles. As an example, we solve the densities for the reactants for power law waiting time and Gaussian jump length, obtain the corresponding fractional aging reaction diffusion equations, and show the dependence of anomalous diffusion of reactants on the age of the process and the reaction rate.