Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds
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.
View Full-Text
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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. https://doi.org/10.3390/fractalfract3040050
AMA Style
Stamov G, Martynyuk A, Stamova I. Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds. Fractal and Fractional. 2019; 3(4):50. https://doi.org/10.3390/fractalfract3040050
Chicago/Turabian StyleStamov, Gani, Anatoliy Martynyuk, and Ivanka Stamova. 2019. "Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds" Fractal and Fractional 3, no. 4: 50. https://doi.org/10.3390/fractalfract3040050
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
