https://doi.org/10.1140/epjp/s13360-022-02421-3
Regular Article
Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model
1
Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203, Cartagena, Spain
2
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia
3
Lab Theor Cosmology, Int Centre of Gravity and Cosmos, TUSUR, 634050, Tomsk, Russia
4
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
5
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, 64002, Douliou, Yunlin, Taiwan, Republic of China
6
Department of Mathematics, Cankaya University, Ankara, Turkey
7
Institute of Space Science, Magurele-Bucharest, Romania
a juan.garcia@upct.es, jlgarcia@kau.edu.sa
Received:
29
November
2021
Accepted:
25
January
2022
Published online:
18
February
2022
This study is to introduce a novel design and implementation of a neuro-swarming computational numerical procedure for numerical treatment of the fractional Bagley–Torvik mathematical model (FBTMM). The optimization procedures based on the global search with particle swarm optimization (PSO) and local search via active-set approach (ASA), while Mayer wavelet kernel-based activation function used in neural network (MWNNs) modeling, i.e., MWNN-PSOASA, to solve the FBTMM. The efficiency of the proposed stochastic solver MWNN-GAASA is utilized to solve three different variants based on the fractional order of the FBTMM. For the meticulousness of the stochastic solver MWNN-PSOASA, the obtained and exact solutions are compared for each variant of the FBTMM with reasonable accuracy. For the reliability of the stochastic solver MWNN-PSOASA, the statistical investigations are provided based on the stability, robustness, accuracy and convergence metrics.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
