Open AccessSolving a class of high-order fractional stochastic heat equations with fractional noise
Author(s) -
Xiaodong Zhang,
Junfeng Liu
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2022593
Subject(s) - uniqueness , mathematics , fractional calculus , class (philosophy) , malliavin calculus , order (exchange) , noise (video) , space (punctuation) , mathematical analysis , gaussian noise , stochastic differential equation , stochastic partial differential equation , type (biology) , pure mathematics , partial differential equation , computer science , algorithm , finance , ecology , biology , artificial intelligence , economics , image (mathematics) , operating system
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.