Composite subdiffusion equation that describes transient subdiffusion.

Abstract

A composite 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 α and D_{α} to subdiffusion with parameters β and D_{β}. The parameters are defined by the time evolution of the mean square displacement of diffusing particle σ^{2}(t)=2D_{i}t^{i}/Γ(1+i), i=α,β. The function g controls the process at intermediate times. The composite subdiffusion equation is more general than the ordinary fractional subdiffusion equation with constant parameters; it has potentially wide application in modeling diffusion processes with changing parameters.