On the estimation of the Lyapunov function in solutions of a quasilinear fractional system

1Martynyuk, AA
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2020, 11:3-8
Section: Mathematics
Language: Ukrainian

Qualitative theory of the equations of perturbed motion with a fractional derivative of the state vector has been developed in the last several years. These studies were initiated by the introduction of a fractional derivative for the Lyapunov function (Martynyuk, 2018). The development of this idea in a number of works has made it possible to create an analogue of the Lyapunov’s theory of stability of motion for fractional systems of equations. This paper is devoted to the consideration of a class of quasilinear systems with a fractional deri vative of the system state vector. For this type of equations, a new estimate of the Lyapunov functions over time on their solutions is obtained.

Keywords: estimation of Lyapunov functions, fractional-like derivative, quasilinear system

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