Eur. Phys. J. B (2017) 90: 70
https://doi.org/10.1140/epjb/e2017-80060-5

Regular Article

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

¹ School of Science, Beijing Technology and Business University, Beijing 100048, P.R. China
² CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
³ Department of Physics, Beijing Normal University, Beijing 100875, P.R. China

^a e-mail: liujian@mail.bnu.edu.cn

Received: 25 January 2017
Received in final form: 22 February 2017
Published online: 12 April 2017

Abstract

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^γ, 0 ≤ γ< 2, and the probability density function ω(t) of a particle’s transition time t follows a power law for large t: ω(t) ~ t^{− (1 + α)},1 <α< 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 ω(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.