The fractional order is introduced into the shape memory alloy oscillator model, and the effect of fractional order on the system dynamics is discussed. Firstly, based on the fractional differential equation theory, the fractional shape memory alloy system (FSMA) is constructed, and the stability of the system and the existence conditions of Hopf bifurcation are presented. Then, a time-delay feedback controller is designed to control the stability of the FSMA system. Finally, the numerical results indicate that the time delay and fractional order play important roles in regulating the dynamic properties of the shape memory alloy system.