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

Andrey Zahariev and Hristo Kiskinov
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Andrey Zahariev: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria
Hristo Kiskinov: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria

Mathematics, 2020, vol. 8, issue 3, 1-18

Abstract: 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.

Keywords: Caputo fractional derivative; neutral linear fractional system; nonlinear perturbation; asymptotic stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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