Lyapunov Stability of Singular Integral Equations via Fourier Methods

Resumo

In this paper, we utilize the Fourier transform to analyze the Lyapunov stability of singular integral equations. By applying this transform, we simplify the stability analysis by converting the singular integral equation into an algebraic form. Additionally, the Fourier transform is used to derive sufficient conditions for the Lyapunov stability of singular integral equations with impulses. Our results provide enhancements over traditional methods, offering a new perspective on the stability evaluation of these equations. The approach is illustrated through several theorems, and lemmas and examples.