APPLICATIONS OF FRACTIONAL CALCULUS IN AI-BASED IMAGE RECOGNITION

Abstract

Fractional calculus has emerged as a powerful mathematical tool capable of capturing long-range dependencies, memory effects, and multi-scale structures that conventional integer-order models cannot represent adequately. In modern AI-based image recognition systems, these properties offer a critical advantage, particularly in complex tasks involving texture discrimination, edge preservation, noise suppression, and feature extraction across heterogeneous image domains. This paper investigates the application of fractional-order operators, fractional differential masks, Caputo and Riemann–Liouville derivatives, and fractional-order neural networks to enhance recognition accuracy and computational robustness. The study centralizes how fractional calculus improves gradient sensitivity, enables adaptive filtering, and provides enhanced feature stability in deep learning frameworks. Fractional-order Laplacians and fractional Fourier transforms further refine spatial–frequency representations, enabling superior performance in low-light, noisy, and medical imaging environments. The review also highlights the increasing integration of fractional-order learning rules in CNNs and GAN-based architectures, improving interpretability and resistance to adversarial distortions. By synthesizing mathematical insights with AI-driven imaging techniques, this paper establishes fractional calculus as a promising theoretical and computational framework capable of redefining next-generation image recognition models. The findings position fractional operators as transformative tools for overcoming limitations of classical differential methods and advancing accuracy, generalization, and computational efficiency in image-based AI systems.