Modeling nonlinear variable-order fractional chaotic systems using the Caputo-Fabrizio operator and radial basis function neural networks.

This study explores the characteristics of a nonlinear fractional chaotic model applying a fractional-order variation approach, leveraging radial basis function neural networks (RBFNN) for efficient modeling. Unlike previous research that relied on constant fractional orders, this work incorporates variable fractional derivatives, allowing the system's memory effects to evolve over time. This adaptability enhances the accuracy and realism of chaotic behavior representation, making it more suitable for dynamic real-world applications. The Caputo-Fabrizio fractional derivative is employed to describe the system's behavior, while RBFNN effectively learns and predicts its complex behavior with reduced computational cost. Compared to fixed-order models, the variable fractional-order formulation offers greater flexibility, better captures transient dynamics, and improves precision in system analysis. Additionally, phase space reconstruction is performed to examine the system's evolution across different fractional orders. Error analysis confirms the reliability of the proposed model, achieving a minimal error threshold below [Formula: see text], demonstrating its robustness in predicting chaotic trajectories. The findings establish the superiority of variable fractional-order modeling and its potential applications in fields such as secure communication, control systems, and signal processing. This research provides a novel and efficient framework for studying nonlinear fractional chaotic systems, opening new possibilities for enhanced system analysis and prediction.