CDq ON THE UNIFORM STABILITY OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS USING VECTOR LYAPUNOV FUNCTIONS

This paper investigates the uniform stability of the trivial solution for nonlinear Caputo fractional differential equations (FrDEs). Unlike traditional approaches that rely on scalar Lyapunov functions (SLFs), this study employs vector Lyapunov functions (VLFs) to analyze the stability properties of these equations. By utilizing comparison results specific to vector FrDEs, the paper establishes sufficient conditions under which uniform stability can be guaranteed. The theoretical findings are further substantiated through two illustrative examples, demonstrating the practical applicability of the derived stability criteria. The results contribute to a deeper understanding of stability in the context of FrDEs and provide a novel methodological framework for addressing complex nonlinear systems in this domain.