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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (6): 94-101.doi: 10.6040/j.issn.1671-9352.0.2021.451

• • 上一篇    

Gronwall不等式的推广及应用

王小焕1,吕广迎1*,戴利杰2   

  1. 1.南京信息工程大学数学与统计学院, 江苏 南京 210044;2.河南大学数学与统计学院, 河南 开封 475001
  • 发布日期:2022-06-10
  • 作者简介:王小焕(1980— ),女,博士,讲师,研究方向为偏微分方程、随机分析. E-mail:003304@nuist.edu.cn *通信作者简介:吕广迎(1982— ),男,教授,研究方向为随机分析、无穷维动力系统. E-mail:gylvmaths@nuist.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11771123;11901158;12171247)

Generalization of Gronwalls inequality and applications

WANG Xiao-huan1, LÜ Guang-ying1*, DAI Li-jie2   

  1. 1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Mathematics and Statistics, Henan University, Kaifeng 475001, Henan, China
  • Published:2022-06-10

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摘要： 推广了经典的Gronwall不等式, 得到了具有多个奇异点的广义Gronwall不等式, 并利用此不等式证明了分数阶随机微分方程组温和解的存在唯一性。

关键词: Gronwall不等式, 分数阶随机微分方程, 唯一性

Abstract: The classical Gronwalls inequality is generalized and a Gronwalls inequality with multiple singularity points is obtained. Then the existence and uniqueness of solutions to stochastic fractional order differential equations is obtained by using the obtained inequality.

Key words: Gronwalls inequality, stochastic fractional differential equations, uniqueness

中图分类号: 

  • O212.1
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