This study proposes a matrix-based collocation method employing sixth-kind Chebyshev polynomials (SKCPs) to explore the dynamics of a fractional-order compartmental model for Glaucoma characterized by progressive damage to the optic nerve and subsequent loss of vision. The pseudo-operational matrices for integration are formulated based on shifted SKCPs over an extended interval \([0, \mathcal{T}]\) , enabling efficient numerical approximation of the model’s solutions. The approximations provide insights into the behavior and interdependencies of the model’s compartmental variables. The theoretical analysis confirms the existence and uniqueness of the solution set via Schauder’s fixed-point theorem. Furthermore, the Ulam–Hyers stability of the approximate solutions is established, ensuring the robustness of the numerical scheme under perturbations. To evaluate model responsiveness, a sensitivity analysis is conducted by varying key parameters, identifying critical factors influencing disease dynamics. A feedback control strategy is integrated into the model to enhance its predictive and corrective capabilities, aiming to inform treatment strategies for improving eye health. This control mechanism is derived from the pseudo-operational collocation method combined with the Lagrange multiplier technique. Lastly, error bounds for the residual functions are rigorously estimated in a Chebyshev-weighted norm, verifying the accuracy and convergence properties of the proposed numerical method.
