Strict uniform stability analysis in terms of two measures of Caputo fractional dynamic systems on time scale

Abstract

This work investigates the (m, m₀)-strict uniform stability of Caputo fractional dynamic systems on time scales, leveraging the Caputo fractional derivative’s ability to model memory and hereditary effects for a more accurate representation of real-world dynamics. Traditional stability concepts, such as Lyapunov and asymptotic stability, often lack the granularity to fully capture complex system behaviors. To address this, we focus on (m, m₀)-strict uniform stability, which provides a stringent and comprehensive framework for analyzing system robustness and convergence rates. Using vector Lyapunov functions, we enable component-wise stability analysis, offering a detailed understanding of multi-dimensional dynamics, particularly in high-dimensional systems with interdependent variables. We also demonstrate the practical relevance of our approach through a comprehensive example.