  Based on the non-Markov diffusion equation taking into account the spatial
fractality and modeling for the generalized coefficient of particle diffusion
$D^{\alpha\alpha'}(\mathbf{r},\mathbf{r}';t,t')=W(t,t')\bar{D}^{\alpha\alpha'}(\mathbf{r},\mathbf{r}')$
using fractional calculus the generalized Cattaneo--Maxwell--type diffusion
equation in fractional time and space derivatives has been obtained. In the
case of a constant diffusion coefficient, analytical and numerical studies of
the frequency spectrum for the Cattaneo--Maxwell diffusion equation in
fractional time and space derivatives have been performed. Numerical
calculations of the phase and group velocities with change of values of
characteristic relaxation time, diffusion coefficient and indexes of temporal
$\xi$ and spatial $\alpha$ fractality have been carried out.
