AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (297.1 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
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
Show Author Information

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

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10625-10650
DOI: 10.3934/math.2022593

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
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

0

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
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)