On the regularity of weak solutions to space-time fractional stochastic heat equations

This study is concerned with the space-time fractional stochastic heat-type equations driven by multiplicative noise, which can be used to model the anomalous heat diffusion in porous media with random effects with thermal memory. We first deduce the weak solutions to the given problem by means of the Laplace transform and Mittag-Leffler function. Using the fractional calculus and stochastic analysis theory, we further prove the pathwise spatial-temporal regularity properties of weak solutions to this type of SPDEs in the framework of Bochner spaces.