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

Abstract

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 Hölder 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.

Keywords

• fractional differential operator
• stochastic partial differential equation
• fractional noise
• hölder continuity
• malliavin calculus