Averaging principle for Hilfer fractional impulsive stochastic evolution equations

LÜ Ting; YANG Min; WANG Qiru

doi:10.13471/j.cnki.acta.snus.2023A006

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Averaging principle for Hilfer fractional impulsive stochastic evolution equations

Research articles | 更新时间：2024-01-25

- Averaging principle for Hilfer fractional impulsive stochastic evolution equations
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 63, Issue 1, Pages: 145-153(2024)
- 作者机构：
  
  1.太原理工大学数学学院，山西太原 030024
  2.中山大学数学学院，广东广州 510275
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2023A006
  CLC： O211.63
- Published：25 January 2024，
  
  Published Online：15 November 2023，
  
  Received：16 January 2023，
  
  Accepted：22 March 2023
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吕婷,杨敏,王其如.Hilfer分数阶脉冲随机发展方程的平均原理[J].中山大学学报(自然科学版)(中英文),2024,63(01):145-153.

LÜ Ting,YANG Min,WANG Qiru.Averaging principle for Hilfer fractional impulsive stochastic evolution equations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(01):145-153.
吕婷,杨敏,王其如.Hilfer分数阶脉冲随机发展方程的平均原理[J].中山大学学报(自然科学版)(中英文),2024,63(01):145-153. DOI： 10.13471/j.cnki.acta.snus.2023A006.

LÜ Ting,YANG Min,WANG Qiru.Averaging principle for Hilfer fractional impulsive stochastic evolution equations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(01):145-153. DOI： 10.13471/j.cnki.acta.snus.2023A006.

摘要

利用分数阶微积分理论、半群性质、不等式技巧和随机分析理论，建立了分数布朗运动驱动的Hilfer分数阶脉冲随机发展方程的平均原理，证明了原方程的适度解均方收敛于无脉冲平均方程的适度解，并通过实例说明了所得理论结果的适用性.

Abstract

By using fractional calculus， semigroup theories， inequality techniques and stochastic analysis theories， an averaging principle for Hilfer fractional impulsive stochastic evolution equations driven by fractional Brownian motion is established. The mild solution of the original equations converges to the mild solution of the reduced averaged equations without impulses in the mean square sense is proved. And an example is presented to illustrate the applicability of our obtained theoretical results.

关键词

平均原理Hilfer分数阶导数脉冲随机发展方程分数布朗运动

Keywords

averaging principleHilfer fractional derivativeimpulsive stochastic evolution equationsfractional Brownian motion

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