Composite subdiffusion equation that describes transient subdiffusion

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 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 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.