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Research Article | Open Access

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

Xiaodong Zhang1, Junfeng Liu2( )
School of Information Engineering, Nanjing Audit University, Nanjing 211815, China
School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
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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 operatorstochastic partial differential equationfractional noiseHölder continuityMalliavin calculus
CLC number: 60G35, 60H07, 60H15

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10625-10650
DOI: 10.3934/math.2022593

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Cite this article:
Zhang X, Liu J. Solving a class of high-order fractional stochastic heat equations with fractional noise. AIMS Mathematics, 2022, 7(6): 10625-10650. https://doi.org/10.3934/math.2022593

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Received: 28 January 2022
Revised: 23 March 2022
Accepted: 24 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)