Space-Time Fractional Stochastic Equations on Regular Bounded Open Domains

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 Holder 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.