Fractional PINNs: new frontiers for long-range memory in continuum models

Abstract

The fundamentals and motivations of Fractional Calculus for describing dynamics with pro- longed memory in both temporal and spatial domains are presented. To overcome the high numerical complexity involved in fractional convolutions, the framework of Physics-Informed Neural Networks (PINNs) is adopted, integrating Laplace and Fourier transforms that convert the memory into simple products in the transformed domain. This work illustrates the potential of PINNs in modeling an arc beam with fractional delay, showing stable convergence and a significant reduction in computational cost. Thus, it lays the foundation for future extensions to more complex geometries and processes, where non-local memory is essential.