A novel design of layered recurrent neural networks for fractional order Caputo–Fabrizio stiff electric circuit models

Abstract

Electrical engineering models often rely on complex circuit configurations that facilitate the dynamic flow of electrically charged particles within a closed conductive network. These circuits serve as essential tools for simulating and analyzing diverse electrical systems and components. This paper introduces a study on nonlinear fractional circuits modeling through the development of a stochastic neuro-computational artificial intelligent-based solver to address mathematical models governing the Fractional order Caputo–Fabrizio stiff electric circuit model (FO-CFSECM) by manipulating the knacks of layered recurrent neural networks (LRNNs) trained with Gradient-based local search algorithm (GLA). In fractional calculus, the Caputo–Fabrizio (CF) fractional order derivative (FOD) emerges as a powerful instrument, binding its capabilities to deliver remarkably accurate solutions for fractional stiff systems. The objective of this work is to exploit the numerical treatment comprehensively for the dynamics of fractal Resistor–Capacitor (RC) and fractal Resistor–Inductor (RL) circuit models by introducing the CF fractional operator. Through the application of artificial intelligence-based soft computing and advanced back-propagative deep neural networks, a deeper understanding of the behavior and distinctive characteristics inherent in these models is sought. The Levenberg–Marquardt optimizer serves as an efficient training GLA tool for learning of LRNNs weights of fractal RL/RC circuit models. The comparative studies on variants of FO-CFSECM demonstrate that LRNNs achieve an impressive mean square error (MSE) ranging from 10[Formula: see text] to 10[Formula: see text] and absolute error (AE) within 10[Formula: see text] to 10[Formula: see text]. The accuracy, reliability, and efficiency of LRNNs for solving the FO-CFSECM were further validated through MSE, AE, controlling parameters of state transitions, error histograms, and correlation measures.