Neural network approximation of the composition of fractional operators and its application to the fractional Euler-Bernoulli beam equation

Anna Nowak, Dominika Kustal, HongGuang Sun and Tomasz Blaszczyk

Applied Mathematics and Computation, 2025, vol. 501, issue C

Abstract: In this paper, we propose a new approach to approximation of the left and the right fractional Riemann - Liouville integrals as well as the compositions of these two operators, based on a shallow neural network with ReLU as an activation function. We apply the proposed method to the fractional Euler - Bernoulli beam equation with fixed-supported and fixed-free ends, and we provide numerical simulations for constant, power and trigonometric functions. Finally, we compare the obtained results with the exact solutions of the considered problems.

Keywords: Neural networks; Fractional Euler-Bernoulli equation; Fractional operators (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:501:y:2025:i:c:s0096300325002012

DOI: 10.1016/j.amc.2025.129475

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