As a critical component of railway infrastructure, the railway point machine (RPM) is vital for the operational efficiency and safety of the entire railway system. The intelligent diagnosis of RPM faults is thus of considerable significance. Traditional methods have often neglected the fractional-order components in fault signals, focusing instead on integer-order signals during feature extraction. This study presents a novel fault diagnosis approach that leverages the vibration signals of the RPM. Utilizing the Fractional Fourier Transform (FRFT) at its optimal order to extract fractional-order features, the subsequent deep learning process employs Convolutional Neural Networks (CNN) to further enhance these extracted features, and finally classifying the fault data with SVM, the method addresses the shortcomings of existing techniques. The effectiveness of this approach is confirmed through experimental results, which demonstrate its ability to accurately identify RPM faults. This advancement in fault diagnosis is expected to significantly enhance the predictive maintenance of railway systems.