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