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

Xiaodong Zhang; Junfeng Liu; Xiaodong Zhang; Junfeng Liu

doi:10.3934/math.2022593

AIMS Mathematics

2022, Volume 7, Issue 6: 10625-10650. doi: 10.3934/math.2022593

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Research article

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

Xiaodong Zhang ¹,
Junfeng Liu ^{2
,
,}

1.
School of Information Engineering, Nanjing Audit University, Nanjing 211815, China
2.
School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China

Received: 28 January 2022 Revised: 23 March 2022 Accepted: 24 March 2022 Published: 30 March 2022
MSC : 60G35, 60H07, 60H15

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.
- fractional differential operator,
- stochastic partial differential equation,
- fractional noise,
- Hölder continuity,
- Malliavin calculus
Citation: Xiaodong Zhang, Junfeng Liu. Solving a class of high-order fractional stochastic heat equations with fractional noise[J]. AIMS Mathematics, 2022, 7(6): 10625-10650. doi: 10.3934/math.2022593

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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.

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