Solving a class of high-order fractional stochastic heat equations with fractional noise

This paper is concerned with a class of high-order fractional stochastic partial differential equations driven by fractional noise. We firstly prove the existence and uniqueness of the mild solution and then study the Holder continuity of the solution with respect to space and time variables. In addition, we also prove the existence and Gaussian-type estimates for the density of the solution by using the techniques of Malliavin calculus.

Automated summary

This paper investigates a class of high-order fractional stochastic partial differential equations driven by fractional noise. The existence and uniqueness of the mild solution are proven, and the Holder continuity of the solution with respect to space and time variables is studied. Additionally, the existence and Gaussian-type estimates for the density of the solution are also demonstrated using Malliavin calculus techniques.