$G$-subdiffusion equation that describes transient subdiffusion

TL;DR

This paper introduces a generalized $g$-subdiffusion equation with a fractional Caputo derivative to model the transition between different subdiffusive regimes, capturing time-dependent changes in diffusion parameters.

Contribution

It proposes a novel $g$-subdiffusion equation that describes the continuous transition between subdiffusive behaviors with varying parameters, extending traditional models.

Findings

The $g$-subdiffusion equation effectively models parameter transitions.

It captures the process of changing diffusion regimes over time.

Potential applications in modeling complex diffusion processes.

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.