Global hypoellipticity and global solvability in Gevrey classes on the n-dimensional torus

We consider an evolution equation with the regularized fractional derivative of an order (alpha)(element of) (0,1) with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables. Such equations describe diffusion on inhomogeneous fractals. A fundamental solution of the Cauchy problem is constructed and investigated.