Open Access

ARTICLE

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

Ashish Rayal¹, Priya Dogra¹, Sabri T. M. Thabet^2,3,4,*, Imed Kedim⁵, Miguel Vivas-Cortez^6,*

1 Department of Mathematics, School of Applied and Life Sciences, Uttaranchal University, Dehradun, 248007, India
2 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, India
3 Department of Mathematics, Radfan University College, University of Lahej, Lahej, 73560, Yemen
4 Department of Mathematics, College of Science, Korea University, Seoul, 02814, Republic of Korea
5 Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia
6 Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Sede Quito, 17-01-2184, Ecuador

* Corresponding Authors: Sabri T. M. Thabet. Email: ; Miguel Vivas-Cortez. Email:

(This article belongs to the Special Issue: Analytical and Numerical Solution of the Fractional Differential Equation)

Computer Modeling in Engineering & Sciences 2025, 143(2), 1895-1925. https://doi.org/10.32604/cmes.2025.060989

Received 14 November 2024; Accepted 27 January 2025; Issue published 30 May 2025

Abstract

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.

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Keywords

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