In this paper, we present a Caputo fractional-order COVID-19 model that incorporates nucleic acid testing and individual protective awareness to capture memory effects and the interaction of non-pharmaceutical interventions. We proved the existence, non-negativity, and boundedness of solutions and derived the basic reproduction number $R_0$ using the next-generation matrix method. Stability analysis showed that the disease-free equilibrium is globally asymptotically stable when $R_0<1$, and the endemic equilibrium is globally asymptotically stable when $R_0>1$. Numerical simulations using the PECE scheme of the Adams–Bashforth–Moulton method validate the theoretical results and demonstrate the role of the fractional-order parameter $\alpha$ in capturing transmission memory. Model parameters were estimated using a hybrid genetic algorithm-least squares approach calibrated with Malaysian COVID-19 data. The proposed model outperformed both integer-order and simplified fractional SEIR models in replicating real-world dynamics. Sensitivity and uncertainty analyses identified protective awareness and testing intensity as key factors in mitigating epidemic severity. We also formulated an optimal control problem, applying Pontryagin's maximum principle to derive six intervention strategies. Cost-effectiveness analysis showed that combined interventions are superior to single strategies, proving effective and economically viable under Malaysia's healthcare constraints.