This paper considers the asymptotic stability of a class of nonlinear fractional order impulsive switched systems by extending the result of existing work. First, a criterion is given to verify the stability of systems by using the Mittag–Leffler function and fractional order multiple Lyapunov functions. Second, by combining the methods of minimum dwell time with fractional order multiple Lyapunov functions, another sufficient condition for the stability of systems is given. Third, by using a periodic switching technique, a switching signal is designed to ensure the asymptotic stability of a system with both stable and unstable subsystems. Finally, two numerical examples are provided to illustrate the theoretical results.