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Volume 7
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10.3390/math7060500
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Article

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

by
Guotao Wang
1,2,
Jianfang Qin
1,*,
Huanhe Dong
2 and
Tingting Guan
1
1
School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China
2
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(6), 500; https://doi.org/10.3390/math7060500
Submission received: 21 April 2019 / Revised: 19 May 2019 / Accepted: 24 May 2019 / Published: 2 June 2019
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems)
Versions Notes

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.
Keywords: generalized Mittag–Leffler stability; Hilfer fractional nonautonomous system; Hilfer type fractional comparison principle; fractional Lyapunov direct method generalized Mittag–Leffler stability; Hilfer fractional nonautonomous system; Hilfer type fractional comparison principle; fractional Lyapunov direct method

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MDPI and ACS Style

Wang, G.; Qin, J.; Dong, H.; Guan, T. Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System. Mathematics 2019, 7, 500. https://doi.org/10.3390/math7060500

AMA Style

Wang G, Qin J, Dong H, Guan T. Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System. Mathematics. 2019; 7(6):500. https://doi.org/10.3390/math7060500

Chicago/Turabian Style

Wang, Guotao, Jianfang Qin, Huanhe Dong, and Tingting Guan. 2019. "Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System" Mathematics 7, no. 6: 500. https://doi.org/10.3390/math7060500

APA Style

Wang, G., Qin, J., Dong, H., & Guan, T. (2019). Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System. Mathematics, 7(6), 500. https://doi.org/10.3390/math7060500

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