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Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System

Author

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  • Guotao Wang

    (School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China
    College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Jianfang Qin

    (School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China)

  • Huanhe Dong

    (College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Tingting Guan

    (School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China)

Abstract

This article studies the generalized Mittag–Leffler stability of Hilfer fractional nonautonomous system by using the Lyapunov direct method. A new Hilfer type fractional comparison principle is also proved. The novelty of this article is the fractional Lyapunov direct method combined with the Hilfer type fractional comparison principle. Finally, our main results are explained by some examples.

Suggested Citation

  • Guotao Wang & Jianfang Qin & Huanhe Dong & Tingting Guan, 2019. "Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System," Mathematics, MDPI, vol. 7(6), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:500-:d:236555
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    References listed on IDEAS

    as
    1. Wang, JinRong & Zhang, Yuruo, 2015. "Nonlocal initial value problems for differential equations with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 850-859.
    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. Wang, Zhen & Xie, Yingkang & Lu, Junwei & Li, Yuxia, 2019. "Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 360-369.
    4. Gu, Haibo & Trujillo, Juan J., 2015. "Existence of mild solution for evolution equation with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 344-354.
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