The Rabinovich–Fabrikant system epitomizes a fundamental construct in nonlinear dynamical systems, where subtle parametric interplays lead to the emergence of intricate chaotic attractors, and an exceptionally sensitive dependence on initial conditions within multifaceted physical contexts. In this paper, we present a fractional-order Rabinovich–Fabrikant (FO–RF) system demonstrating chaotic attractor-like behavior under different fractional orders and parameter sets. This characterization is achieved through a twofold approach: first, an efficient Caputo fractional differentiation-based Adams multistep PECE solver is incorporated to numerically treat the nonlinear FO-RF systems; second, a nonlinear AutoRegressive eXogenous (ARX) temporal neuro-structure is devised to simulate, analyze and characterize the ensuing chaotic dynamics. The numerical outcomes are prepared for the nonlinear ARX neural network characterization through a time-based partitioning into training, validation and testing sets, with optimized temporal feature learning through a Bayesian Regularized Levenberg Marquardt backpropagation (BRLM-BP-ARX) algorithm. These predicted sequences are rigorously evaluated against their numerical counterparts with analysis on iterative error convergence charts, regression reports, correlation infographics, and sequential temporal responses. Additionally, a thorough comparative error analysis for the simulated FO-RF solutions is carried out. To further assess the temporal feature learning robustness, the BRLM-BP-ARX neural network’s one-step-ahead and multi-step-ahead forecasting capabilities are tested for the intricate FO-RF chaotic dynamics. The empirical results from exhaustive experiments showcase that the BRLM-BP-ARX framework attains diminutive errors, spanning from 10–7 to 10–12, underscoring effectiveness of the approach for intricate fractional-order nonlinear dynamical systems.
