{"title":"定义了ψ-分数阶微分系统的Lyapunov指数","authors":"N'Gbo N'Gbo, Jianhua Tang","doi":"10.1115/1.4057041","DOIUrl":null,"url":null,"abstract":"\n In this article, we focus on the relations between the asymptotics of solutions and the sensitivity to initial values of fractional differential systems. To investigate this problem, we consider the ψ-fractional calculus, which is considered to be a generalization of those of Riemann-Liouville and Hadamard. For this purpose, we define Lyapunov exponents for ψ-fractional differential systems and estimate their upper bounds. Examples are also presented to demonstrate the efficiency of our results.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"49 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Define the Lyapunov Exponents for ψ-Fractional Differential System\",\"authors\":\"N'Gbo N'Gbo, Jianhua Tang\",\"doi\":\"10.1115/1.4057041\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n In this article, we focus on the relations between the asymptotics of solutions and the sensitivity to initial values of fractional differential systems. To investigate this problem, we consider the ψ-fractional calculus, which is considered to be a generalization of those of Riemann-Liouville and Hadamard. For this purpose, we define Lyapunov exponents for ψ-fractional differential systems and estimate their upper bounds. Examples are also presented to demonstrate the efficiency of our results.\",\"PeriodicalId\":54858,\"journal\":{\"name\":\"Journal of Computational and Nonlinear Dynamics\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Nonlinear Dynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4057041\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4057041","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Define the Lyapunov Exponents for ψ-Fractional Differential System
In this article, we focus on the relations between the asymptotics of solutions and the sensitivity to initial values of fractional differential systems. To investigate this problem, we consider the ψ-fractional calculus, which is considered to be a generalization of those of Riemann-Liouville and Hadamard. For this purpose, we define Lyapunov exponents for ψ-fractional differential systems and estimate their upper bounds. Examples are also presented to demonstrate the efficiency of our results.
期刊介绍:
The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.