Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model
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
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
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