Guirao Juan L G, Sabir Zulqurnain, Raja Muhammad Asif Zahoor, Baleanu Dumitru
Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203 Cartagena, Spain.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589 Saudi Arabia.
Eur Phys J Plus. 2022;137(2):245. doi: 10.1140/epjp/s13360-022-02421-3. Epub 2022 Feb 18.
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.
本研究旨在介绍一种新颖的神经群体计算数值程序的设计与实现，用于对分数阶巴格利 - 托尔维克数学模型（FBTMM）进行数值处理。基于粒子群优化（PSO）的全局搜索和通过活动集方法（ASA）的局部搜索的优化程序，同时在神经网络（MWNNs）建模中使用基于迈耶小波核的激活函数，即MWNN - PSOASA，来求解FBTMM。所提出的随机求解器MWNN - GAASA的效率被用于基于FBTMM的分数阶求解三种不同的变体。为了确保随机求解器MWNN - PSOASA的精确性，将FBTMM每个变体的所得解与精确解进行比较，具有合理的准确性。为了验证随机求解器MWNN - PSOASA 的可靠性，则基于稳定性、鲁棒性、准确性和收敛度量进行统计研究。
