{"title":"Discrete fractional-order Halanay inequality with mixed time delays and applications in discrete fractional-order neural network systems","authors":"Xiang Liu, Yongguang Yu","doi":"10.1007/s13540-025-00395-4","DOIUrl":null,"url":null,"abstract":"<p>In this paper, which can be considered as an extension of our previous publication (Liu and Yu in Fract Calc Appl Anal 25:2040-2061, 2022) in same journal, we analyze the stability and synchronization for the discrete fractional-order neural network systems with mixed time delays. By new techniques, we give the proof of the discrete fractional-order Halanay inequality with mixed time delays, which contains both discrete and distributed time delays. Then, using this fractional-order Halanay inequality and constructing an appropriate Lyapunov function, we give the sufficient criteria of Mittag-Leffler stability and synchronization for the discrete fractional-order neural network systems with mixed time delays. Finally, an example is provided to illustrated one of the results.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"48 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-03-31","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/s13540-025-00395-4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, which can be considered as an extension of our previous publication (Liu and Yu in Fract Calc Appl Anal 25:2040-2061, 2022) in same journal, we analyze the stability and synchronization for the discrete fractional-order neural network systems with mixed time delays. By new techniques, we give the proof of the discrete fractional-order Halanay inequality with mixed time delays, which contains both discrete and distributed time delays. Then, using this fractional-order Halanay inequality and constructing an appropriate Lyapunov function, we give the sufficient criteria of Mittag-Leffler stability and synchronization for the discrete fractional-order neural network systems with mixed time delays. Finally, an example is provided to illustrated one of the results.
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.
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