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Open AccessArticle

Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds

by Gani Stamov 1,†,‡, Anatoliy Martynyuk 2,‡ and Ivanka Stamova 3,*,‡
1
Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria
2
S.P. Timoshenko Institute of Mechanics, NAS of Ukraine, 03057 Kiev-57, Ukraine
3
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
*
Author to whom correspondence should be addressed.
Current address: University of Texas at San Antonio, San Antonio, TX 78249, USA.
These authors contributed equally to this work.
Fractal Fract 2019, 3(4), 50; https://doi.org/10.3390/fractalfract3040050
Received: 21 September 2019 / Revised: 1 November 2019 / Accepted: 4 November 2019 / Published: 7 November 2019
(This article belongs to the Special Issue 2019 Selected Papers from Fractal Fract’s Editorial Board Members)
In this paper, an impulsive fractional-like system of differential equations is introduced. The notions of practical stability and boundedness with respect to h-manifolds for fractional-like differential equations are generalized to the impulsive case. For the first time in the literature, Lyapunov-like functions and their derivatives with respect to impulsive fractional-like systems are defined. As an application, an impulsive fractional-like system of Lotka–Volterra equations is considered and new criteria for practical exponential stability are proposed. In addition, the uncertain case is also investigated.
Keywords: fractional-like derivative; impulses; practical stability; boundedness; h-manifolds fractional-like derivative; impulses; practical stability; boundedness; h-manifolds
MDPI and ACS Style

Stamov, G.; Martynyuk, A.; Stamova, I. Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds. Fractal Fract 2019, 3, 50.

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