Stability of a Fractional Opinion Formation Model with and without Leadership Using the New Generalized Hattaf Fractional Derivative

4区工程技术 Q1 Mathematics

Mathematical Problems in Engineering Pub Date : 2024-04-23 DOI:10.1155/2024/6652993

M. Ait Ichou, K. Hattaf

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.

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使用新广义哈塔夫分式导数的有领导力和无领导力分式舆论形成模型的稳定性

在本文中，我们提出并分析了两种舆论形成模型的动态行为，一种是有领导力模型，另一种是无领导力模型。所提出的两个模型都是在新的广义哈塔夫分数（GHF）导数框架下用分数微分方程（FDE）表示的。两个模型都严格建立了 Mittag-Leffler 意义上的稳定性。充分研究了代理意见向共识意见的收敛性。我们还给出了数值模拟来说明分析结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Problems in Engineering 工程技术-工程：综合

CiteScore

4.00

自引率

0.00%

发文量

2853

审稿时长

4.2 months

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.