  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.
