Regular Article

Aging continuous time random walks with A → B reaction

¹ Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Cheng’du, Si’chuan 610059, P.R. China
² Department of Mathematics, Dali Prefecture Experimental Middle School, Dali, Yunnan 671000, P.R. China

^a e-mail: zhanghong13@cdut.cn

Received: 30 August 2018
Received in final form: 3 April 2019
Published online: 10 June 2019

Abstract

Aging continuous time random walk (ACTRW) which describes a dynamical process starting at time − t_a 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.