Stability analysis of Abel's equation of the first kind

This paper established sufficient conditions for the stability of Abel's differential equation of the first kind. These conditions explicate the impact of the asymptotic behaviors exhibited by the time-varying coefficients on the overall stability of the system. More precisely, we studied the p...

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Bibliographic Details
Published in:	AIMS mathematics Vol. 8; no. 12; pp. 30574 - 30590
Main Authors:	Naser, Mohammad F.M., Aal, Mohammad Abdel, Gumah, Ghaleb
Format:	Journal Article
Language:	English
Published:	AIMS Press 01-01-2023
Subjects:	abel's equation asymptotic stability attractivity boundedness of solutions uniform stability
Online Access:	Get full text
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Summary:	This paper established sufficient conditions for the stability of Abel's differential equation of the first kind. These conditions explicate the impact of the asymptotic behaviors exhibited by the time-varying coefficients on the overall stability of the system. More precisely, we studied the positivity, the continuation and the boundedness of solutions. Additionally, we investigated the attractivity, the asymptotic stability, the uniform stability and the instability of the system. The results were scrutinized by numerical simulations.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.20231563