This paper explores chaotic behaviour in a fractional-order Tuberculosis model, utilizing Caputo derivatives to capture essential memory and hereditary effects in disease transmission. To address real-world uncertainties and external perturbations, the paper uses a robust fractional-order adaptive sliding mode control strategy within a master-slave synchronization framework. A fractional-order disturbance observer is integrated to estimate unknown bounded disturbances, while hybrid projective synchronization allows for flexible scaling between systems. Validated through MATLAB simulations, the results prove that this fractional approach outperforms integer-order models in accuracy and stability. This framework offers significant potential for advancing disease forecasting, epidemic control, and secure communication systems.