# Stochastic Burgers equation with fractional derivative driven by multiplicative noise

## TL;DR

This paper investigates the existence, uniqueness, and regularity of solutions to a fractional stochastic Burgers equation driven by multiplicative noise, using advanced stochastic analysis, fractional calculus, and semigroup theory.

## Contribution

It introduces new results on the well-posedness and regularity of fractional stochastic Burgers equations with multiplicative noise, expanding understanding in this complex area.

## Key findings

- Proved existence and uniqueness of mild solutions.
- Established regularity properties of solutions.
- Applied stochastic analysis, fractional calculus, and semigroup theory.

## Abstract

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.