This paper focuses on the analysis of multiple types of time delays and fractional-order proportional-derivative (PDα) controller on the dynamics of fractional-order p53 model. The multiple types of time delay schemes are dexterously designed during the bifurcation control for the proposed system, and the comparative study is elaborately performed on bifurcation control theoretically. Analysis reveals that the negative feedback delay restrains the delay threshold, while the positive feedback delay promotes the delay threshold and makes the system more robust. System dynamics is affected by fractional order, which is more conducive to the generation of system oscillations. We have adapted control system techniques and designed a PDα controller. This controller is used to activate p53 protein. Numerical results display that the addition of PDα controller can increase the richness of the dynamic system. The differential gain parameter kd of PDα controller promotes the appearance of oscillation, and the proportional gain parameter kp will hinder the appearance of oscillation. The PD controller is a good strategy to control the oscillation behaviors of the system.
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