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 and D_ to subdiffusion with parameters and D_. The parameters are defined by the time evolution of the mean square displacement of diffusing particle ^2 (t) =2D₈t^i/ (1+i), i=,. 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.