  Fractional (in time and in space) evolution equations defined on Dirichlet
regular bounded open domains, driven by fractional integrated in time Gaussian
spatiotemporal white noise, are considered here. Sufficient conditions for the
definition of a weak-sense Gaussian solution, in the mean-square sense, are
derived. The temporal, spatial and spatiotemporal H\"older continuity, in the
mean-square sense, of the formulated solution is obtained, under suitable
conditions, from the asymptotic properties of the Mittag-Leffler function, and
the asymptotic order of the eigenvalues of a fractional polynomial of the
Dirichlet negative Laplacian operator on such bounded open domains.
