Stochastic Burgers equation with fractional derivative driven by multiplicative noise
Provides theoretical foundations for fractional stochastic PDEs, but the result is incremental as it generalizes existing techniques to a new equation class.
Proved existence, uniqueness, and regularity of mild solutions for a time- and space-fractional stochastic Burgers equation with multiplicative noise, extending known results to a more general fractional setting.
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. We also proved the regularity properties of mild solution for this generalized Burgers equation.