Reaction Subdiffusion with Random Waiting Time Depending on the Preceding Jump Length**Supported by the National Natural Science Foundation of China under Grant No 11626047, and the Foundation for Young Key Teachers of Chengdu University of Technology under Grant No KYGG201414.

Abstract

To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction under subdiffsion with waiting time depending on the preceding jump length, and derive the corresponding master equations in the Fourier–Laplace space for the distribution of A and B particles in a continuous time random walk scheme. Moreover, the generalizations of the reaction-diffusion equation for the Gaussian jump length with the probability density function of waiting time being quadratically dependent on the preceding jump length are obtained by applying the derived master equations.