Fractional Order Turbidostat Model with the Discrete Delay of Digestion

In this paper, we consider the turbidostat system with fractional delayed differential equations.Stability of the unique positive equilibrium point of the systems with and without delay areinvestigated.We prove the existence of Hopf bifurcation for delayed case. Then, the influenceof fractional order and time delay parameter on the system is examined through numericalsimulations.