$G$-subdiffusion equation that describes transient subdiffusion

Abstract

A $g$--subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ is used to describe a process of a continuous transition from subdiffusion with parameters $\alpha$ and $D_{\alpha }$ to subdiffusion with parameters $\beta$ and $D_{\beta }$. The parameters are defined by the time evolution of the mean square displacement of diffusing particle ${\sigma }^2(t)=2D_i{t}^i/\Gamma (1+i)$, $i=\alpha ,\beta$. The function $g$ controls the process at "intermediate" times. The $g$--subdiffusion equation is more general than the "ordinary" fractional subdiffusion equation with constant parameters, it has potentially wide application in modelling diffusion processes with changing parameters.

5 pages, 4 figures

Cited by in corpus (1)

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