This paper investigates the dynamics and control of a fractional-order delayed predator–prey system with disease in the prey. The existence conditions for all feasible equilibria are analyzed. The local asymptotic stability of these equilibria is then studied by deriving the characteristic equation and establishing the corresponding stability criterion. Furthermore, it is demonstrated that the system undergoes a Hopf bifurcation as the time delay crosses a critical threshold, leading to the emergence of sustained periodic oscillations. To suppress oscillations and control disease transmission, a time-delayed feedback controller is incorporated into the infected prey dynamics. Theoretical analysis reveals that the additional control delay can elevate the critical threshold. Numerical simulations validate this strategy, highlighting its potential for ecological management.
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