Abstract: A class of integer order memristor chaotic system is extended to fractional order. Firstly, numerical simulations are carried out, then circuit of the system is designed in Multisim software, and the circuit simulation results are consistent with the numerical simulation results. Next, according to the active control principle and the stability theory of fractional order systems, taking the fractional order memristor chaotic system and fractional Liu system as the control objects, the controllers are designed, and the synchronization of the two systems with different dimensions and different structures are studied by the methods of dimension increase. Finally, the two synchronization circuits are realized in Multisim software, and the simulation results show the effectiveness of the controller. The design and implementation of fractional memristor chaotic system and its synchronization circuits studied in this paper can be combined with simulation software for teaching, which makes the abstract theory teaching vivid and concrete, and provides new ideas and methods for the teaching of nonlinear system theory, nonlinear circuit design and other courses.