{"title":"Discrete fractional calculus with exponential memory: Propositions, numerical schemes and asymptotic stability","authors":"Guang Yang, Guo-Cheng Wu, Hui Fu","doi":"10.15388/amc.2024.29.33550","DOIUrl":null,"url":null,"abstract":"A new fractional difference with an exponential kernel function is proposed in this study. First, a difference operator is defined by the exponential function. From the Cauchy problem of the nth-order difference equation, new fractional-order sum and differences are presented. The propositions between each other and numerical schemes are derived. Finally, fractional linear difference equations are presented, and exact solutions are given by using a new discrete Mittag-Leffler function.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Modelling and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15388/amc.2024.29.33550","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A new fractional difference with an exponential kernel function is proposed in this study. First, a difference operator is defined by the exponential function. From the Cauchy problem of the nth-order difference equation, new fractional-order sum and differences are presented. The propositions between each other and numerical schemes are derived. Finally, fractional linear difference equations are presented, and exact solutions are given by using a new discrete Mittag-Leffler function.
期刊介绍：
The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology.
The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.
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