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The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems
Open AccessArticle

Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation

Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria
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Mathematics 2020, 8(3), 390; https://doi.org/10.3390/math8030390
Received: 30 January 2020 / Revised: 4 March 2020 / Accepted: 7 March 2020 / Published: 10 March 2020
(This article belongs to the Special Issue Stability Analysis of Fractional Systems)
In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general solution of a linear autonomous neutral system with several delays is established and used for the study of the stability properties of a neutral autonomous nonlinear perturbed linear fractional differential system. Natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system. View Full-Text
Keywords: Caputo fractional derivative; neutral linear fractional system; nonlinear perturbation; asymptotic stability Caputo fractional derivative; neutral linear fractional system; nonlinear perturbation; asymptotic stability
MDPI and ACS Style

Zahariev, A.; Kiskinov, H. Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation. Mathematics 2020, 8, 390.

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