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Finite time stability of tempered fractional systems with time delays

Author

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  • Zitane, Hanaa
  • Torres, Delfim F.M.

Abstract

We investigate the notion of finite time stability for tempered fractional systems (TFSs) with time delays and variable coefficients. Then, we examine some sufficient conditions that allow concluding the TFSs stability in a finite time interval, which include the nonhomogeneous and the homogeneous delayed cases. We present two different approaches. The first one is based on Hölder’s and Jensen’s inequalities, while the second one concerns the Bellman–Grönwall method using the tempered Grönwall inequality. Finally, we provide two numerical examples to show the practicability of the developed procedures.

Suggested Citation

  • Zitane, Hanaa & Torres, Delfim F.M., 2023. "Finite time stability of tempered fractional systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011670
    DOI: 10.1016/j.chaos.2023.114265
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    References listed on IDEAS

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    1. Chuan-Yun Gu & Feng-Xia Zheng & Babak Shiri, 2021. "Mittag-Leffler Stability Analysis Of Tempered Fractional Neural Networks With Short Memory And Variable-Order," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-12, December.
    2. Hamdi Gassara & Dhouha Kharrat & Abdellatif Ben Makhlouf & Lassaad Mchiri & Mohamed Rhaima, 2023. "SOS Approach for Practical Stabilization of Tempered Fractional-Order Power System," Mathematics, MDPI, vol. 11(13), pages 1-10, July.
    3. Jingwei Deng & Weiyuan Ma & Kaiying Deng & Yingxing Li, 2020. "Tempered Mittag–Leffler Stability of Tempered Fractional Dynamical Systems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, May.
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