具有非 Lipschitz 条件的随机卡普托分数微分方程的平均原理

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-08-14 DOI:10.1007/s13540-024-00308-x

Zhongkai Guo, Xiaoying Han, Junhao Hu

{"title":"具有非 Lipschitz 条件的随机卡普托分数微分方程的平均原理","authors":"Zhongkai Guo, Xiaoying Han, Junhao Hu","doi":"10.1007/s13540-024-00308-x","DOIUrl":null,"url":null,"abstract":"<p>In this paper, the averaging principle for stochastic Caputo fractional differential equations with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence and uniqueness of solution. And finally, the averaging principle is considered.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition\",\"authors\":\"Zhongkai Guo, Xiaoying Han, Junhao Hu\",\"doi\":\"10.1007/s13540-024-00308-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, the averaging principle for stochastic Caputo fractional differential equations with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence and uniqueness of solution. And finally, the averaging principle is considered.</p>\",\"PeriodicalId\":48928,\"journal\":{\"name\":\"Fractional Calculus and Applied Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractional Calculus and Applied Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13540-024-00308-x\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Calculus and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00308-x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文考虑了非线性项满足非 Lipschitz 条件的随机 Caputo 分微分方程的平均原理。文章的工作大致分为三个部分。首先，我们建立了具有奇异积分核的广义 Gronwall 不等式，这是我们分析的关键部分。其次，我们讨论了解的存在性和唯一性。最后，考虑平均原理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition

In this paper, the averaging principle for stochastic Caputo fractional differential equations with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence and uniqueness of solution. And finally, the averaging principle is considered.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.