A Lyapunov-based approach to uniform strict stability analysis for nonlinear impulsive Caputo fractional derivatives with weakly singular kernel

Povzetek

This study explores the uniform strict stability of nonlinear impulsive Caputo fractional differential equations (ICFrDEs) by utilizing a powerful framework of vector Lyapunov functions which is generalized by a class of piecewise continuous Lyapunov functions. By integrating comparison results and employing this new class of Lyapunov functions, comprehensive sufficient conditions for uniform strict stability are derived. The applicability and significance of these findings are illustrated through a detailed example, which demonstrates the improvements over existing results and highlights the broader implications of this approach. This research contributes significantly to the analysis of uniform strict stability of ICFrDEs, providing a robust framework for future studies.