In this chapter, a fractional order ratio-dependent predator–prey system with time delay, where the dynamics is logistic with the carrying capacity proportional to prey population, is studied. Mainly, a Hopf bifurcation parameter is taken as the time delay, the local stability of a positive equilibrium and the presence of Hopf bifurcations are determined. Moreover, by defining Lyapunov function for this system, global stability of the solution are proven. Finally, to support our new theoretical results, two different numerical examples are illustrated, choosing two different fractional orders q.