This paper explores the application of fractional calculus in image processing, focusing on image enhancement and denoising. Fractional calculus, which extends traditional calculus to include non-integer orders, offers unique benefits in these areas. The authors delve into the foundational theories of fractional calculus, including its amplitude-frequency characteristics, and evaluate the effectiveness of fractional differential and integral operators in enhancing image features and reducing noise. Key findings include: 1. **Image Enhancement**: Fractional-order differential operators outperform integer-order operators in enhancing image details such as weak edges and strong textures. These operators act as high-pass filters, amplifying medium to high-frequency signals nonlinearly. 2. **Image Denoising**: Fractional-order integral operators excel in denoising images by attenuating high-frequency signals, improving the signal-to-noise ratio (SNR) while preserving essential features like edges and textures. These operators act as low-pass filters, with their effectiveness increasing as the integration order rises. The study provides empirical results demonstrating the advantages of fractional calculus-based image processing techniques over traditional methods. Future research directions include adaptive fractional-order image processing and the integration of fractional calculus with advanced intelligent algorithms.This paper explores the application of fractional calculus in image processing, focusing on image enhancement and denoising. Fractional calculus, which extends traditional calculus to include non-integer orders, offers unique benefits in these areas. The authors delve into the foundational theories of fractional calculus, including its amplitude-frequency characteristics, and evaluate the effectiveness of fractional differential and integral operators in enhancing image features and reducing noise. Key findings include: 1. **Image Enhancement**: Fractional-order differential operators outperform integer-order operators in enhancing image details such as weak edges and strong textures. These operators act as high-pass filters, amplifying medium to high-frequency signals nonlinearly. 2. **Image Denoising**: Fractional-order integral operators excel in denoising images by attenuating high-frequency signals, improving the signal-to-noise ratio (SNR) while preserving essential features like edges and textures. These operators act as low-pass filters, with their effectiveness increasing as the integration order rises. The study provides empirical results demonstrating the advantages of fractional calculus-based image processing techniques over traditional methods. Future research directions include adaptive fractional-order image processing and the integration of fractional calculus with advanced intelligent algorithms.