{"title":"可能的 Lyapunov 函数的分数差分不等式：综述","authors":"Yiheng Wei, Linlin Zhao, Xuan Zhao, Jinde Cao","doi":"10.1007/s13540-024-00298-w","DOIUrl":null,"url":null,"abstract":"<p>This study delves into the origin, evolution, and practical applications of fractional difference inequalities based on recent literature. The review provides an overview of existing inequalities proposed under various definitions. Furthermore, to enhance this potent mathematical tool, a series of new inequalities have been introduced. Additionally, leveraging renowned Lyapunov functions in continuous-time domain, their discrete-time counterparts have been formulated. Moreover, several new potential Lyapunov functions have been identified. This review aims to aid readers in selecting suitable inequalities and Lyapunov functions to analyze the stability of nabla fractional order systems.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractional difference inequalities for possible Lyapunov functions: a review\",\"authors\":\"Yiheng Wei, Linlin Zhao, Xuan Zhao, Jinde Cao\",\"doi\":\"10.1007/s13540-024-00298-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This study delves into the origin, evolution, and practical applications of fractional difference inequalities based on recent literature. The review provides an overview of existing inequalities proposed under various definitions. Furthermore, to enhance this potent mathematical tool, a series of new inequalities have been introduced. Additionally, leveraging renowned Lyapunov functions in continuous-time domain, their discrete-time counterparts have been formulated. Moreover, several new potential Lyapunov functions have been identified. This review aims to aid readers in selecting suitable inequalities and Lyapunov functions to analyze the stability of nabla fractional order systems.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-06-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13540-024-00298-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00298-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Fractional difference inequalities for possible Lyapunov functions: a review
This study delves into the origin, evolution, and practical applications of fractional difference inequalities based on recent literature. The review provides an overview of existing inequalities proposed under various definitions. Furthermore, to enhance this potent mathematical tool, a series of new inequalities have been introduced. Additionally, leveraging renowned Lyapunov functions in continuous-time domain, their discrete-time counterparts have been formulated. Moreover, several new potential Lyapunov functions have been identified. This review aims to aid readers in selecting suitable inequalities and Lyapunov functions to analyze the stability of nabla fractional order systems.
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