A Numerical Study of the Caputo Fractional Nonlinear Rössler Attractor Model via Ultraspherical Wavelets Approach

The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns, biological systems, and secure communications. So, this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets. The Caputo fractional Rössler attractor model is simulated into two categories, (i) Asymmetric and (ii) Symmetric. The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model, depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics. Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method. Also, the stability analyses of the considered model are discussed for different equilibrium points. Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica. The suggested approach can solve another non-linear fractional model due to its straightforward implementation.