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<p>The primary focus of this study is to apply the Fourier transform technique to address the stability problem of higher-order linear differential equations. Another key aspect is the investigation of the Hyers-Ulam stability of linear differential equations using the Fourier transform method. Furthermore, the results are extended to the Hyers-Ulam-Mittag-Leffler stability of these equations. From an applied perspective, the Fourier transform is employed to determine the Ulam stabilities of differential equations arising in mass-spring systems, with the results illustrated through graphical representations.</p>

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Stability Analysis of Higher-Order Linear Differential Equations Using the Fourier Transform With Applications

  • 期刊论文

  • 发表日期：

    2025年4月30日

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  • M. Sivashankar,
  • S. Sabarinathan,
  • Salah Boulaaras,
  • Mohamed Abdalla,
  • Taha Radwan

摘要

The primary focus of this study is to apply the Fourier transform technique to address the stability problem of higher-order linear differential equations. Another key aspect is the investigation of the Hyers-Ulam stability of linear differential equations using the Fourier transform method. Furthermore, the results are extended to the Hyers-Ulam-Mittag-Leffler stability of these equations. From an applied perspective, the Fourier transform is employed to determine the Ulam stabilities of differential equations arising in mass-spring systems, with the results illustrated through graphical representations.