多孔介质问题的 Mittag-Leffler 稳定性和 Lyapunov 稳定性

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-06-05 DOI:10.1007/s13540-024-00299-9

Jamilu Hashim Hassan, Nasser-eddine Tatar, Banan Al-Homidan

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引用次数: 0

摘要

研究了多孔介质中出现的分数阶问题。讨论了问题的好拟性和稳定性。在位移分量中存在强分数阻尼和体积分数分量中存在分数摩擦阻尼的情况下，证明了 Mittag-Leffler 稳定性。这将现有的整数阶（二阶）结果扩展到了非整数阶。在体积分数分量中不存在分数阻尼的情况下，可以证明其趋近于零且具有李亚普诺夫均匀稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Mittag-Leffler stability and Lyapunov stability for a problem arising in porous media

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Mittag-Leffler stability and Lyapunov stability for a problem arising in porous media

A fractional order problem arising in porous media is considered. Well-posedness as well as stability are discussed. Mittag-Leffler stability is proved in case of a strong fractional damping in the displacement component and a fractional frictional one in the volume fraction component. This extends an existing result from the integer-order (second-order) case to the non-integer case. In the absence of the fractional damping in the volume fraction component, it is shown a convergence to zero and a Lyapunov uniform stability.

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.