可能的 Lyapunov 函数的分数差分不等式：综述

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-06-12 DOI:10.1007/s13540-024-00298-w

Yiheng Wei, Linlin Zhao, Xuan Zhao, Jinde Cao

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引用次数: 0

摘要

本研究以最新文献为基础，深入探讨了分数差分不等式的起源、演变和实际应用。综述概述了在各种定义下提出的现有不等式。此外，为了增强这一强大的数学工具，还引入了一系列新的不等式。此外，利用连续时间域中著名的 Lyapunov 函数，还提出了离散时间域中的对应函数。此外，还确定了几个新的潜在 Lyapunov 函数。本综述旨在帮助读者选择合适的不等式和 Lyapunov 函数来分析 nabla 分数阶系统的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Fractional difference inequalities for possible Lyapunov functions: a review

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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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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.