SUMMARY
Time delay of economic policy and memory property in a real economy system is omnipresent and inevitable. In this paper, a business cycle model with fractional-order time delay which describes the delay and memory property of economic control is investigated. Stochastic averaging method is applied to obtain the approximate analytical solution. Numerical simulations are done to verify the method. The effects of the fractional order, time delay, economic control and random excitation on the amplitude of the economy system are investigated. The results show that time delay, fractional order and intensity of random excitation can all magnify the amplitude and increase the volatility of the economy system.