涉及媒体的Atangana-Baleanu分数谣言传播模型的最优控制与动态分析

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-07-12 DOI:10.1016/j.nonrwa.2025.104457

Guotao Wang, Ningning Huang, Lihong Zhang

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引用次数: 0

摘要

近年来，如何有效地控制谣言的传播一直是公众关注的热点问题之一。数学模型可以为这一问题提供定量分析和决策支持。本文建立了一个具有Atangana-Baleanu分数阶导数的社交网络谣言传播模型，该模型包括权威媒体报道的影响和媒体的转化机制。验证了所考虑系统解的基本性质和系统的Ulam稳定性。为了使控制谣言的成本最小化，利用庞特里亚金斯极大值原理，提出了一种实时最优控制模型。最后给出了数值模拟结果，分析了不同参数对Atangana-Baleanu分数谣言传播模型的影响，验证了模型的真实性和有效性。

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Optimal control and dynamic analysis of a new Atangana–Baleanu fractional rumor dissemination model involving media

In recent years, how to control the spreading of rumors effectively has been one of the public hot issues. Mathematical models can provide quantitative analysis and decision support for this problem. In this paper, a rumor dissemination model with the Atangana–Baleanu fractional derivative in social networks is established, which includes the influence of authoritative media reports and the transformation mechanism of media. The basic properties of the solution for the considered system and the Ulam stability of the system are verified. In order to minimize the cost of controlling rumors, a real-time optimal control model is also proposed by using the Pontryagins maximum principle. At last, numerical simulation results are given to analyze the impacts of different parameters on the Atangana–Baleanu fractional rumor dissemination model, which indicates that our model is realistic and effective.

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.