Strict mittag-leffler stability of fractional unperturbed systems

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2026-06-01 Epub Date: 2026-01-16 DOI:10.1016/j.cnsns.2026.109757

Dilara Karslıoğlu , Coşkun Yakar

引用次数: 0

Abstract

This study concentrates on investigating strict Mittag-Leffler stability for fractional differential systems operating without external perturbations. The focus is on unperturbed systems, where the dynamics are solely intrinsic and free from outside influences. Utilizing Caputo fractional derivatives alongside a suitably constructed Lyapunov-like functional, we establish new sufficient conditions guaranteeing that solutions converge strictly to the equilibrium point. The findings offer a sharper and more detailed description of stability than classical asymptotic notions, emphasizing the significance of memory properties inherent in fractional-order models. Several illustrative examples are provided to demonstrate the practical applicability and robustness of the derived criteria in such autonomous systems.

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分数阶无摄动系统的严格mittag-leffler稳定性

本文主要研究无外部扰动的分数阶微分系统的严格Mittag-Leffler稳定性。重点是无扰动系统，其中动态完全是内在的，不受外界影响。利用Caputo分数阶导数和适当构造的lyapunov泛函，我们建立了保证解严格收敛于平衡点的新的充分条件。这些发现提供了比经典渐近概念更清晰、更详细的稳定性描述，强调了分数阶模型中固有的记忆特性的重要性。给出了几个说明性的例子来证明所导出的准则在这种自治系统中的实际适用性和鲁棒性。

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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.