Generalized Master Equation for Space-Time Coupled Continuous Time Random Walk

The generalized master equation for the space-time coupled continuous time random walk is derived analytically,in which the space-time coupling is considered through the correlated function g(t)~t~γ,0≤γ< 2, and the probability density function ω(t) of a particle’s waiting time t follows a power law form for large t: ω(t)~t~(-(1+α)),0 <α< 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent γ and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.