{"title":"Stability of a Fractional Opinion Formation Model with and without Leadership Using the New Generalized Hattaf Fractional Derivative","authors":"M. Ait Ichou, K. Hattaf","doi":"10.1155/2024/6652993","DOIUrl":null,"url":null,"abstract":"In this paper, we propose and analyze the dynamical behaviors of two opinion formation models, one with leadership and the other without leadership. The two proposed models are formulated by fractional differential equations (FDEs) with the frame of the new generalized Hattaf fractional (GHF) derivative. The stability in the sense of Mittag–Leffler is rigorously established for both models. The convergence of agents’ opinions to the consensus opinion is fully investigated. Numerical simulations are given to illustrate the analytical results.","PeriodicalId":18319,"journal":{"name":"Mathematical Problems in Engineering","volume":"27 3","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Problems in Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1155/2024/6652993","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose and analyze the dynamical behaviors of two opinion formation models, one with leadership and the other without leadership. The two proposed models are formulated by fractional differential equations (FDEs) with the frame of the new generalized Hattaf fractional (GHF) derivative. The stability in the sense of Mittag–Leffler is rigorously established for both models. The convergence of agents’ opinions to the consensus opinion is fully investigated. Numerical simulations are given to illustrate the analytical results.
期刊介绍：
Mathematical Problems in Engineering is a broad-based journal which publishes articles of interest in all engineering disciplines. Mathematical Problems in Engineering publishes results of rigorous engineering research carried out using mathematical tools. Contributions containing formulations or results related to applications are also encouraged. The primary aim of Mathematical Problems in Engineering is rapid publication and dissemination of important mathematical work which has relevance to engineering. All areas of engineering are within the scope of the journal. In particular, aerospace engineering, bioengineering, chemical engineering, computer engineering, electrical engineering, industrial engineering and manufacturing systems, and mechanical engineering are of interest. Mathematical work of interest includes, but is not limited to, ordinary and partial differential equations, stochastic processes, calculus of variations, and nonlinear analysis.
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