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

Guotao Wang, Jianfang Qin, Huanhe Dong and Tingting Guan
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Guotao Wang: School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, 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

Mathematics, 2019, vol. 7, issue 6, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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