|Title||On the estimation of the Lyapunov function in solutions of a quasilinear fractional system|
|Publication Type||Journal Article|
|Year of Publication||2020|
|Abbreviated Key Title||Dopov. Nac. akad. nauk Ukr.|
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|
1. Abdeljawad, T. (2015). On conformable fractional calculus. J. Comput. Appl. Math., 279, pp. 57-66.
2. Anderson, D. R. & Ulness, D. J. (2016). Results for conformable differential equations: preprint. Concordia College, Moorhead, MN.
3. Khalil, Al Horani, M., Yousef, A. & Sababheh, M. (2014). A new definition of fractional derivative. J. Comput. Appl. Math., 264, pp. 65-70.
4. Martynyuk, A. A. & Martynyuk-Chernienko, Yu. A. (2020). Boundedness of the solutions of fractional-like equations of perturbed motions. Int. Appl. Mech., 56, No. 5.
5. Martynyuk, A. А. (2018). On stability analysis of fractional-like systems of perturbed motion. Dopov. Nac. akad. nauk Ukr., No. 6, pp. 9-16 (in Russian). https://doi.org/10.15407/dopovidi2018.06.009
6. Martynyuk, A. A. & Stamova, I. M. (2018). Fractional-like derivative of Lyapunov-type functions and applications to the stability analysis of motion. Electron. J. Differ. Equ., 2018, No. 62, pp. 1-12.
7. Martynyuk, A. A., Stamov, G. & Stamova, I. M. (2019). Practical stability analysis with respect to manifolds and boundedness of differential equations with fractional-like derivatives. Rocky Mt. J. Math., 49, No. 1, pp. 211-233.
8. Stamov, G., Martynyuk, A. & Stamova, I. (2019). Impulsive fractional-like diffrential equations: practical stability and boundedness with respect to h-manifolds. Fractal Fract., 3, No. 4, 50. https://doi.org/10.3390/fractalfract3040050
9. Stamov, G., Stamova, I., Martynyuk, A. & Stamov, T. (2020). Design and practical stability of а new class of impulsive fractional-like neural networks. Entropy, 22, 337. https://doi.org/10.3390/e22030337