Abstract
This research explores the various chaotic features of the hyperchaotic Chen dynamical system within a variable order fractional (VOF) calculus framework, employing an innovative approach with a nonlinear and adaptive radial basis function neural network. The study begins by computing the numerical solution of VOF differential equations for the hyperchaotic Chen system through a numerical scheme using the Caputo-Fabrizio derivative across a spectrum of different system control parameters. Subsequently, a comprehensive parametric model is formulated using RBFNN, considering the system's various initial values. We systematically investigate the various chaotic attractors of the proposed system, employing statistical analysis, phase space reconstruction, and Lyapunov exponent. Additionally, we assess the effectiveness of the proposed computational RBFNN model using the Root Mean Square Error statistic. Importantly, the obtained results closely align with those derived from numerical algorithms, emphasizing the high accuracy and reliability of the designed network. The outcomes of this study have implications for studying chaos with variable fractional derivatives, with applications across various scientific and engineering domains. This work advances the understanding and applications of variable order fractional dynamics.