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Tempered Mittag–Leffler Stability of Tempered Fractional Dynamical Systems

Author

Listed:
  • Jingwei Deng
  • Weiyuan Ma
  • Kaiying Deng
  • Yingxing Li

Abstract

Due to finite lifespan of the particles or boundedness of the physical space, tempered fractional calculus seems to be a more reasonable physical choice. Stability is a central issue for the tempered fractional system. This paper focuses on the tempered Mittag–Leffler stability for tempered fractional systems, being much different from the ones for pure fractional case. Some new lemmas for tempered fractional Caputo or Riemann–Liouville derivatives are established. Besides, tempered fractional comparison principle and extended Lyapunov direct method are used to construct stability for tempered fractional system. Finally, two examples are presented to illustrate the effectiveness of theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:7962542
    DOI: 10.1155/2020/7962542
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    Cited by:

    1. Zitane, Hanaa & Torres, Delfim F.M., 2023. "Finite time stability of tempered fractional systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Ravi P. Agarwal & Snezhana Hristova & Donal O’Regan, 2023. "Inequalities for Riemann–Liouville-Type Fractional Derivatives of Convex Lyapunov Functions and Applications to Stability Theory," Mathematics, MDPI, vol. 11(18), pages 1-23, September.
    3. Kucche, Kishor D. & Mali, Ashwini D. & Fernandez, Arran & Fahad, Hafiz Muhammad, 2022. "On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. 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.

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