Design of intelligent neuro-structures optimized with Levenberg–Marquardt and Bayesian distribution for dynamical analysis of Caputo–Fabrizio fractional electric circuit models

Electrical engineering models utilize interconnected circuits that consist of charged particles to enable the simulation and study of electric devices and systems, taking advantage of effective electron transfer across a completed circuit. Electric circuits involving the Caputo-Fabrizio (CF) fractional derivative have been precisely modeled recently by known solutions, efficiently capturing the system's response. The paper talks about the application of electrical circuit models for analyzing fractional stiff differential equations in an effort to explore different properties of the fractal Resistor-Capacitor (RC) and Resistor-Inductor (RL) circuits. The study employs artificial intelligence-based neurocomputing techniques and backpropagation networks for the purposes of increasing the knowledge on fractal circuit models. The Bayesian Regularization backpropagated neural networks (BR-BNNs) and Levenberg–Marquardt backpropagated neural networks (LM-BNNs) are utilized as efficient procedure for the training. The mathematical equations of CF-fractional RC and RL circuits were implemented to generate synthetic reference datasets and these information's were then used as a target for execution of LM-BNNs and BR-BNNs to find approximate solutions for the models. To validate and compare the accuracy of BR-BNNs and LM-BNNs in solving CF-fractional electric circuit models, the convergence curves on iterative adaptation of mean squared error (MSE) are employed. Results show that BR-BNNs yields MSE of approximately 10⁻¹² to 10⁻¹³ and absolute error within the range of 10⁻⁶ to 10⁻⁸, which providing strong evidence for the effectiveness of BR-BNNs approach than that of LM-BNNs algorithm. To further validate and endorse precision of the results, a performance evaluation via absolute error, statistical instance distribution in error histogram, regression analysis, convergence stability test, and Wilcoxon signed-rank test were exploited for CF-fractional electric circuit models that shows the statistical adequacy.