Transient bi-fractional diffusion: space-time coupling inducing the coexistence of two fractional diffusions

Abstract

© 2017, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg. Anomalous diffusion is researched within the framework of the coupled continuous time random walk model, in which the space-time coupling is considered through the correlated function g(t) ~ t?, 0 = ?< 2, and the probability density function ?(t) of a particle’s transition time t follows a power law for large t: ?(t) ~ t- (1 + a),1 <a< 2. The bi-fractional generalized master equation is derived analytically which can be applied to describe the transient bi-fractional diffusion phenomenon which is induced by the space-time coupling and the asymptotic behavior of ?(t). Numerical results show that for the transient bi-fractional diffusion, there is a transition from one fractional diffusion to another one in the diffusive process.