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Stability analysis for generalized fractional differential systems and applications

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  • Ren, Jing
  • Zhai, Chengbo

Abstract

This paper shows solicitude for the stability analysis issue of a class of generalized fractional differential systems via fractional comparison principle and Lyapunov direct method. With the concept of (Generalized) Mittag-Leffler (M-L) stability given, we first establish a new framework to consider the global M-L stability of generalized fractional differential systems with or without time-delay, in which new stability criterion is achieved by some novel differential inequalities satisfied by the fractional derivative of Lyapunov functions. Second, through the employment of less conservative comparison principle for the generalized fractional system, a sufficient theorem for the (Generalized) M-L stability is derived. Third, a generalized fractional memristor-based impulsive neural network is investigated to illustrate the proposed stability theory, this model is more general which includes a memristor-based Caputo fractional neural network or common Hopfield neural network as special cases. In the end, two simple numerical examples are listed to affirm the theoretical findings.

Suggested Citation

  • Ren, Jing & Zhai, Chengbo, 2020. "Stability analysis for generalized fractional differential systems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304070
    DOI: 10.1016/j.chaos.2020.110009
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    References listed on IDEAS

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    1. Yang, Dan & Wang, JinRong & O’Regan, D., 2018. "A class of nonlinear non-instantaneous impulsive differential equations involving parameters and fractional order," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 654-671.
    2. Liu, Kui & Wang, JinRong & Zhou, Yong & O’Regan, Donal, 2020. "Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Li, Hui & Kao, YongGui, 2019. "Mittag-Leffler stability for a new coupled system of fractional-order differential equations with impulses," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 22-31.
    4. Shuo Zhang & Yongguang Yu & Wei Hu, 2014. "Robust Stability Analysis of Fractional-Order Hopfield Neural Networks with Parameter Uncertainties," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-14, April.
    5. Baleanu, Dumitru & Wu, Guo–Cheng & Zeng, Sheng–Da, 2017. "Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 99-105.
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    1. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.

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