标题： 基于分数阶方法的内存驱动的有界置信意见动力学：一种基于赫格塞曼-克拉瑟模型的分析 显示英文标题

标题： Memory-Driven Bounded Confidence Opinion Dynamics: A Hegselmann-Krause Model Based on Fractional-Order Methods

摘要： 记忆效应在社会互动和决策过程中起着至关重要的作用。 本文提出了一种新的分数阶有界置信意见动力学模型，以表征系统状态中的记忆效应。 基于赫格尔曼-克拉默框架和分数阶差分，建立了全面的模型，捕捉了历史信息的持续影响。 通过严格的理论分析，研究了包括收敛性和共识性在内的基本特性。 结果表明，与经典的意见动力学相比，所提出的模型不仅保持了良好的收敛性和共识特性，还解决了诸如有界意见单调性等局限性。 这使得对现实场景中意见演化的更真实表示成为可能。 本研究的发现为理解意见形成和演化提供了新的见解和方法论途径，具有理论意义和实际应用价值。 显示英文摘要

摘要： Memory effects play a crucial role in social interactions and decision-making processes. This paper proposes a novel fractional-order bounded confidence opinion dynamics model to characterize the memory effects in system states. Building upon the Hegselmann-Krause framework and fractional-order difference, a comprehensive model is established that captures the persistent influence of historical information. Through rigorous theoretical analysis, the fundamental properties including convergence and consensus is investigated. The results demonstrate that the proposed model not only maintains favorable convergence and consensus characteristics compared to classical opinion dynamics, but also addresses limitations such as the monotonicity of bounded opinions. This enables a more realistic representation of opinion evolution in real-world scenarios. The findings of this study provide new insights and methodological approaches for understanding opinion formation and evolution, offering both theoretical significance and practical applications.