On Total Stability Analysis of Caputo Fractional Dynamic Equations on Time Scale

A. This study explores the total stability of Caputo fractional dynamic equations on time scales, bridging discrete and continuous dynamics.By extending the Caputo fractional delta Dini derivative, it introduces T1-total stability and T2-total stability criteria to address bounded perturbations in initial conditions and system parameters.The framework unifies and extends existing stability concepts, effectively handling hybrid systems with gradual and abrupt changes.Rigorous proofs and illustrative examples demonstrate the practical implications of the theory, highlighting its applicability.