Abstract
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.
Highlights
The fractional Bagley–Torvik mathematical model (FBTMM) has achieved the huge attention of the research community in recent years
The parameter optimization, i.e., weights, for the Mayer wavelet neural network (MWNN) models are obtained using the hybridization of computing procedures of particle swarm intelligence particle swarm optimization (PSO) as an efficacious global search aided with active set algorithms (ASAs) for efficient local refinement mechanism to solve the variants of FBTMM in equation (1)
The solutions of three different variants based on the FBTMM are provided by using the integrated design heuristics of MWNN-PSOASA
Summary
The fractional Bagley–Torvik mathematical model (FBTMM) has achieved the huge attention of the research community in recent years. The numerical, approximate and analytical form of the FBTMM has been performed by many scientists and reported in [6–10]. ⎪⎪⎩ dβ v(τ ) aβ , β 0, 1, dτβ where aα indicates the initial conditions, λ represents the derivative based on the fractional-order with 1.25, 1.5, and 1.75, v(τ ) is the solution of above Eq (1), while a1, a2, and a3 are the constant values The FBTMM represented in Eq (1) was the pioneering work of Bagley and Torvik introducing on the motion of an absorbed plate using the Newtonian fluid [3]
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