The present study proposes a fractional order prey-predator model with Beddington-DeAngelis functional response, that the Caputo fractional derivative is applied. There is exploration of the solutions' existence, uniqueness, non-negativity, and boundedness. Stability of all feasible equilibrium points is determined locally by the use of Matignon's condition. Moreover, we also provide sufficient conditions to assure global asymptotic stability for both the predator-extinction equilibrium point and the positive equilibrium point, with selecting a relevant Lyapunov function and the incidence of Hopf-bifurcation is also displayed. Finally, the fractional order effect on the stability behavior of systems is investigated theoretically and also illustrated numerically to support theoretical results.