Continuous Dependence on the Initial Functions and Stability Properties in Hyers–Ulam–Rassias Sense for Neutral Fractional Systems with Distributed Delays

Autor:	Hristo Kiskinov, Mariyan Milev, Magdalena Veselinova, Andrey Zahariev
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	fractional derivatives neutral fractional systems distributed delay integral representation Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 7, Iss 10, p 742 (2023)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract7100742
Popis:	We study several stability properties on a finite or infinite interval of inhomogeneous linear neutral fractional systems with distributed delays and Caputo-type derivatives. First, a continuous dependence of the solutions of the corresponding initial problem on the initial functions is established. Then, with the obtained result, we apply our approach based on the integral representation of the solutions instead on some fixed-point theorems and derive sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of the investigated systems. A number of connections between each of the Hyers–Ulam, Hyers–Ulam–Rassias, and finite-time Lyapunov stability and the continuous dependence of the solutions on the initial functions are established. Some results for stability of the corresponding nonlinear perturbed homogeneous fractional linear neutral systems are obtained, too.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/1dacf05ec547423d8bcb09f3b0405091 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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