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Inverse Mittag-Leffler stability of structural derivative nonlinear dynamical systems

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  • Hu, D.L.
  • Chen, W.
  • Liang, Y.J.

Abstract

The logarithmic time evolution is widely observed in laboratory and field measurements. However, logarithmic stability has not been well considered till now. In this paper, the definition of Lyapunov stability, including logarithmic and inverse Mittag-Leffler stabilities, is proposed. And via the Lyapunov direct method, the stability of nonlinear dynamical systems based on the structural derivative is investigated. Furthermore, the comparison principle based on the structural derivative is presented in order to obtain the stability conditions for nonlinear dynamical systems. Finally, two demonstrative examples are given to test the proposed stability concept.

Suggested Citation

  • Hu, D.L. & Chen, W. & Liang, Y.J., 2019. "Inverse Mittag-Leffler stability of structural derivative nonlinear dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 304-308.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:304-308
    DOI: 10.1016/j.chaos.2019.04.027
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    References listed on IDEAS

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    1. Shaher Momani & Samir Hadid, 2004. "Lyapunov stability solutions of fractional integrodifferential equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-5, January.
    2. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    3. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
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