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Volume 34, Issue 1
The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises

Yuanyuan Jing, Zhi Li & Liping Xu

DOI: 10.4208/jpde.v34.n1.4

J. Part. Diff. Eq., 34 (2021), pp. 51-66.

Published online: 2021-01

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  • Abstract

The purpose of this paper is to establish an averaging principle for stochastic fractional partial differential equation of order $α > 1$ driven by a fractional noise. We prove the existence and uniqueness of the global mild solution for the considered equation by the fixed point principle. The solutions for SPDEs with fractional noises can be approximated by the solution for the averaged stochastic systems in the sense of $p$-moment under some suitable assumptions.

  • Keywords

Averaging principle, Stochastic fractional partial differential equation, fractional noises.

  • AMS Subject Headings

26A33 60G15 60H15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jingyy120920@163.com (Yuanyuan Jing)

lizhi_csu@126.com (Zhi Li)

xlp211@126.com (Liping Xu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-34-51, author = {Jing , YuanyuanLi , Zhi and Xu , Liping}, title = {The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {1}, pages = {51--66}, abstract = {

The purpose of this paper is to establish an averaging principle for stochastic fractional partial differential equation of order $α > 1$ driven by a fractional noise. We prove the existence and uniqueness of the global mild solution for the considered equation by the fixed point principle. The solutions for SPDEs with fractional noises can be approximated by the solution for the averaged stochastic systems in the sense of $p$-moment under some suitable assumptions.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v34.n1.4}, url = {http://global-sci.org/intro/article_detail/jpde/18554.html} }
TY - JOUR T1 - The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises AU - Jing , Yuanyuan AU - Li , Zhi AU - Xu , Liping JO - Journal of Partial Differential Equations VL - 1 SP - 51 EP - 66 PY - 2021 DA - 2021/01 SN - 34 DO - http://doi.org/10.4208/jpde.v34.n1.4 UR - https://global-sci.org/intro/article_detail/jpde/18554.html KW - Averaging principle, Stochastic fractional partial differential equation, fractional noises. AB -

The purpose of this paper is to establish an averaging principle for stochastic fractional partial differential equation of order $α > 1$ driven by a fractional noise. We prove the existence and uniqueness of the global mild solution for the considered equation by the fixed point principle. The solutions for SPDEs with fractional noises can be approximated by the solution for the averaged stochastic systems in the sense of $p$-moment under some suitable assumptions.

Jing , YuanyuanLi , Zhi and Xu , Liping. (2021). The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises. Journal of Partial Differential Equations. 34 (1). 51-66. doi:10.4208/jpde.v34.n1.4
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