Stochastic Burgers' equation with fractional derivative driven by multiplicative noise

This article is devoted to the study of the existence and uniqueness of mild solution to time- and space-fractional stochastic Burgers' equation perturbed by multiplicative white noise. The required results are obtained by stochastic analysis techniques, fractional calculus and semigroup theory. Moreover, we prove the regularity properties of mild solution to this generalized Burgers' equation in the framework of Bochner spaces.