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

  • Jian Liu
  • Yaohui Zhu
  • Peisong He
  • Xiaosong Chen
  • Jing-Dong Bao
Regular Article

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) ~ tγ, 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.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Jian Liu
    • 1
    • 2
  • Yaohui Zhu
    • 1
  • Peisong He
    • 1
  • Xiaosong Chen
    • 2
  • Jing-Dong Bao
    • 3
  1. 1.School of Science, Beijing Technology and Business UniversityBeijingP.R. China
  2. 2.CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of SciencesBeijingP.R. China
  3. 3.Department of PhysicsBeijing Normal UniversityBeijingP.R. China

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