For a class of time-varying switched systems, when considering the fractional order characteristics of subsystems, finite time stability condition and asynchronous switching control strategy are proposed based on model dependent average dwell time method.With the help of Caputo fractional derivative lemma and switched Lyapunov function, a sufficient condition for the finite time stability of fractional time-varying switched systems is proposed by using matrix inequality technology and the result of finite time stability is further extended to the case of finite time boundedness.A sufficient condition for finite time boundedness of fractional order time-varying switched systems is proposed using the idea of average dwell time and the asynchronous switching controller of the system is designed based on this condition.The proposed design method transforms the asynchronous switching control problem into the solution of matrix inequalities.The effectiveness of the proposed control method is verified by numerical simulation.