Electron. J. Differential Equations, Vol. 2018 (2018), No. 62, pp. 1-12.

Fractional-like derivative of Lyapunov-type functions and applications to stability analysis of motion

Anatoliy A. Martynyuk, Ivanka M. Stamova

Abstract:
This article discusses the application of a fractional-like derivative of Lyapunov-type functions in the stability analysis of solutions of perturbed motion equations with a fractional-like derivative of the state vector. The main theorems of the direct Lyapunov method for this class of motion equations are established.

Submitted February 12, 2018. Published March 6, 2018.
Math Subject Classifications: 34A08, 34D20, 34E20.
Key Words: Fractional-like derivative; Lyapunov method; stability; asymptotic stability; instability.

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Anatoliy A. Martynyuk
S.P. Timoshenko Institute of Mechanics NAS of Ukraine
3 Nesterov str. 03057, Kiev-57, Ukraine
email: center@inmech.kiev.ua
Ivanka M. Stamova
Department of Mathematics
University of Texas at San Antonio
One UTSA Circle, San Antonio, TX 78249, USA
email: ivanka.stamova@utsa.edu

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