Research article

Stability analysis of Abel's equation of the first kind

  • 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.

    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

    Related Papers:

  • 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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