{"title":"涉及广义卡普托分数导数的具有时变延迟的分数模糊微分方程的有限时间稳定性分析","authors":"Lai Van Phut","doi":"10.1007/s13370-024-01201-9","DOIUrl":null,"url":null,"abstract":"<div><p>The main results of this paper are to discuss the primary results of fuzzy differential equations with time-varying delay (FDDEs) via the generalized Caputo fractional derivative. We establish the existence of a unique solution for FDDEs using the method of steps and the generalized Gronwall inequality. Sufficient conditions are proposed to ensure the finite-time stability (FTS) of FDDEs. Finally, we explore specific examples to illustrate and reinforce the results obtained.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finite-time stability analysis of fractional fuzzy differential equations with time-varying delay involving the generalized Caputo fractional derivative\",\"authors\":\"Lai Van Phut\",\"doi\":\"10.1007/s13370-024-01201-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The main results of this paper are to discuss the primary results of fuzzy differential equations with time-varying delay (FDDEs) via the generalized Caputo fractional derivative. We establish the existence of a unique solution for FDDEs using the method of steps and the generalized Gronwall inequality. Sufficient conditions are proposed to ensure the finite-time stability (FTS) of FDDEs. Finally, we explore specific examples to illustrate and reinforce the results obtained.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-024-01201-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01201-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Finite-time stability analysis of fractional fuzzy differential equations with time-varying delay involving the generalized Caputo fractional derivative
The main results of this paper are to discuss the primary results of fuzzy differential equations with time-varying delay (FDDEs) via the generalized Caputo fractional derivative. We establish the existence of a unique solution for FDDEs using the method of steps and the generalized Gronwall inequality. Sufficient conditions are proposed to ensure the finite-time stability (FTS) of FDDEs. Finally, we explore specific examples to illustrate and reinforce the results obtained.
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