Most of the physical phenomena in the nature exist in the form of fractional order

and integer order equation is just a special case of fractional order equation. Compared with the integer order model

the fractional order model is closer to the real world and has a more attractive development prospect. In order to enrich the types of multi-wing chaotic attractors that coexist in fractional chaotic systems

a novel 3D fractional chaotic system is proposed in this paper. The most significant feature of the system is that there is a coexistence of multiple types of multi-wings chaotic attractors

namely the coexistence of two-wing

three-wing

and four-wing chaotic attractors. The dynamic characteristics of the system were analyzed via numerical simulations of phase diagram

Lyapunov exponent spectrum

and bifurcation diagram. A necessary condition for the existence of chaotic attractors was given

which is q>0.822 4. For fixed system parameters

when q=0.98

there is a coexistence of two-wing

two-wing

and four-wing chaotic attractors in the system; when q=0.83

there is a coexistence of two-wing

three-wing

and four-wing chaotic attractors

which indicates that the chaotic characteristics of the system are complex. The simulation results of an analog circuit of the system by the Multisim were consistent with those by the numerical analysis

which further verified the chaotic behaviors of the system. Based on the fractional Lyapunov stability theory and Theorem 1

an adaptive synchronous controller was designed. The simulation shows that the response system and the drive system reached the synchronization within the range of 0.2 s

and the identification of unknown parameters was completed within the range of 0.2 s

thus the controller is effective.