Stability analysis of Abel's equation of the first kind

Mohammad F.M. Naser; Mohammad Abdel Aal; Ghaleb Gumah; Mohammad F.M. Naser; Mohammad Abdel Aal; Ghaleb Gumah

doi:10.3934/math.20231563

AIMS Mathematics

2023, Volume 8, Issue 12: 30574-30590. doi: 10.3934/math.20231563

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Research article

Stability analysis of Abel's equation of the first kind

1.
Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan
2.
Faculty of Arts and Educational Sciences, Middle East University, Amman 11831, Jordan

Received: 06 August 2023 Revised: 20 October 2023 Accepted: 25 October 2023 Published: 10 November 2023
MSC : 93D05, 93D20, 34E10, 34C60

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.
- Abel's equation,
- attractivity,
- asymptotic stability,
- uniform stability,
- boundedness of solutions
Citation: Mohammad F.M. Naser, Mohammad Abdel Aal, Ghaleb Gumah. Stability analysis of Abel's equation of the first kind[J]. AIMS Mathematics, 2023, 8(12): 30574-30590. doi: 10.3934/math.20231563

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Abstract

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.

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