The frequency invariance and phase shift of the first-order steady state moment of system response are deduced for fractional order linear oscillator. Moreover, through the theoretical analysis, the amplification effect of fractional order linear system on the amplitude of first-order steady state moment is verified in stochastic resonance mechanism. Duffing detector is used to realize weak signal detection based on parameter perturbation sensitivity and noise immunity of chaos. Numerical simulations show that this scheme can effectively extract the weak sinusoidal signal from the strong colored noise background and significantly reduce the signal-to-noise ratio threshold in comparison with traditional chaotic detection method.