Fractional Calculus in Machine Learning: A Comprehensive Literature Review

Abstract

Fractional calculus generalizes classical differentiation and integration to non-integer orders, enabling models to incorporate long-range dependencies and memory effects. These properties are increasingly relevant in machine learning, especially for problems involving dynamic, nonlocal, or complex systems. This review surveys the mathematical foundations of fractional calculus, its integration into various machine learning paradigms, performance advantages over traditional methods, and the open challenges that motivate future research.