Solving Time-Fractional Nonlinear Variable-Order Delay PDEs Using Feedforward Neural Networks

Authors

Hala S. Alruhaili, Faculty of Education and Arts, Sohar University, Sohar, OmanFollow
Adel S. Hussain, Administrative & Financial Aairs Department, Al-Iraqia University, Baghdad, IraqFollow
Abdullah M. S. Ajlouni, Department of Basic Sciences, AL-Huson University College, AL-Balqa Applied University, Salt 19117, JordanFollow
Funda Türk, Department of Mathematics, Faculty of Science, Bartýn University, Bartýn, TurkeyFollow
Emad A. Az-Zo’bi, Department of Mathematics and Statistics, Faculty of Science, Mutah University, Mutah P.O. Box 7, Al Karak 61710, JordanFollow
Mohammad A. Tashtoush, Department of Basic Sciences, AL-Huson University College, AL-Balqa Applied University, Salt 19117, Jordan AND Faculty of Education and Arts, Sohar University, Sohar, OmanFollow

Abstract

This study presents an innovative application of Feedforward Neural Networks ‘FNNs’ to solve Variable-Order Fractional Partial Differential Equations ‘VO-FPDEs’ with time delays. Utilizing the Caputo definition, the variable-order fractional derivatives are approximated in terms of integer-order derivatives. The problem is reformulated as a system of partial differential equations with delay terms, which is then addressed using ‘FNNs’ to achieve explicit approximate solutions. Comprehensive error and convergence analyses validate the method’s precision and reliability. The effectiveness of the proposed approach is highlighted through numerical examples, with graphical and tabular representations showcasing minimal absolute errors and robust convergence. These results demonstrate the proposed method’s efficiency and simplicity, establishing it as a powerful tool for addressing complex fractional delay problems.

Recommended Citation

Alruhaili, Hala S.; Hussain, Adel S.; Ajlouni, Abdullah M. S.; Türk, Funda; Az-Zo’bi, Emad A.; and Tashtoush, Mohammad A. (2025) "Solving Time-Fractional Nonlinear Variable-Order Delay PDEs Using Feedforward Neural Networks," Iraqi Journal for Computer Science and Mathematics: Vol. 6: Iss. 3, Article 12.
DOI: https://doi.org/10.52866/2788-7421.1284
Available at: https://ijcsm.researchcommons.org/ijcsm/vol6/iss3/12