Novel Approximation Approach to Fractional Rössler System Illustrating Chaotic Behavior Using the Variational Iteration Method

This study presents a novel approximation approach for the Fractional Rössler System using the Variational Iteration Method (VIM). The Fractional Rössler System, an extension of the classical Rössler System, incorporates fractional-order derivatives to capture more intricate dynamical behaviors. VIM is employed due to its efficiency in handling nonlinear fractional differential equations (FDEs) and its novel application to this system. A comparative analysis with the Adams-Bashforth-Moulton method has been conducted, and numerical values are presented to validate the effectiveness of VIM. The graphical results reveal significant chaotic dynamics, including the presence of strange attractors and sensitivity to initial conditions and bifurcation phenomena indicating transitions between periodic and chaotic regimes. This work provides a new perspective on approximating fractional chaotic systems, demonstrating the potential of VIM in advancing the study of complex dynamical systems.