We propose a fractional-order system resonance method for enhancing the weak characteristics of raw signals. The system response amplitude is used as the evaluation index. Based on this, the optimal value of a fractional order is found to achieve the system resonance. By analyzing the system responses, weak low-frequency signals can apparently be enhanced. Both numerical and approximate analytical solutions are used to certify the accuracy and validity of the method. However, if an excitation is a high-frequency signal, the signal cannot usually be favorably enhanced by the system with small system parameters. Nevertheless, a re-scaled method allows us to seek appropriate matching parameters to achieve the enhancement of the high-frequency signal. Two intuitional studies on the high-frequency harmonic signal and bearing fault simulated signal are performed to verify the effectiveness of the re-scaled method. By processing the experimental bearing fault signals, the results indicate that the amplitude at the fault frequency is greatly amplified and those at other frequencies are obviously suppressed simultaneously. It shows excellent performances in the bearing fault recognition. In addition, we compare the fractional-order system resonance with stochastic resonance (SR) and vibrational resonance (VR), respectively. The excellent performance of the proposed new method is shown.