On the estimation of the Lyapunov function in solutions of a quasilinear fractional system
DOI:
https://doi.org/10.15407/dopovidi2020.11.003Keywords:
estimation of Lyapunov functions, fractional-like derivative, quasilinear systemAbstract
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.
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