Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 49, pp. 1-20.

Title: Stochastic Burgers equations with fractional derivative driven by fractional noise
       
Authors: Yubo Duan (School of Mathematical Sciences, Nankai Univ., Tianjin, China)
         Yiming Jiang (School of Mathematical Sciences, Nankai Univ., Tianjin, China)
         Yang Tian (School of Mathematical Sciences, Nankai Univ., Tianjin, China)
         Yawei Wei (School of Mathematical Sciences and LPMC, Nankai Univ., Tianjin, China)

Abstract:
In this article, we study fractional stochastic Burgers equations perturbed
by fractional noise. Existence and uniqueness of a mild solution is given by
a fixed point argument. Then, we explore Holder regularity of the mild
solution in $C([0,T_{*}];L^p(\Omega;\dot{H}^{\gamma}))$ for some stopping
time $T_{*}$.

Submitted May 25, 2023. Published July 17, 2023.
Math Subject Classifications: 60H15, 35R60, 35K05.
Key Words: Stochastic Burgers equation; Caputo derivative; fractional noise; Mittag-Leffler operator; mild solution.