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

Author

Listed:
  • Nowak, Anna
  • Kustal, Dominika
  • Sun, HongGuang
  • Blaszczyk, Tomasz

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.

Suggested Citation

  • Nowak, Anna & Kustal, Dominika & Sun, HongGuang & Blaszczyk, Tomasz, 2025. "Neural network approximation of the composition of fractional operators and its application to the fractional Euler-Bernoulli beam equation," Applied Mathematics and Computation, Elsevier, vol. 501(C).
    • Handle: RePEc:eee:apmaco:v:501:y:2025:i:c:s0096300325002012
    DOI: 10.1016/j.amc.2025.129475
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