<p>This study presents an extensive mathematical framework for the stability analysis and validation of advanced control applications in continuous, nonlinear, hybrid, and Caputo–Fabrizio fractional-order systems. The proposed methodology integrates Lyapunov theory, Input-to-State Stability analysis, passivity, and small-gain techniques into a cohesive, generalizable criterion suitable for both linear and nonlinear dynamics. The method covers systems that are defined by Caputo–Fabrizio fractional derivatives and can handle uncertainty, disturbances, and mixed events. Validation is part of the stability analysis, which combines proof-based assurances with verification through simulation in real-world conditions. Scenario-based probabilistic analysis links the results of Monte Carlo tests to formal risk limitations. This makes it possible to verify that stability and contract compliance are both fully assured. Case studies featuring robotic manipulators, process control with model predictive control, and adaptive aeronautical systems demonstrate the methodology, achieving significant robustness margins and statistical performance assurance. This unified technique provides a theoretically robust and empirically substantiated pathway from controller synthesis to implementation.</p>