A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative

Authors

  • Kaouther Boulehmi Department of Mathematics, Faculty of Science, AL-Baha University, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i1.5043

Keywords:

Numerical solution, the Atangana-Baleanu , fractional derivative , Initial value problems, Chaos

Abstract

This study aims to use a novel scheme for the Atangana-Baleanu Caputo fractional derivative (ABC-FD) to solve the fractional Bernoulli equation and the fractional R ̈ossler model. Furthermore, the suggested technique is compared to Runge-Kutta Fourth Order (RK4). The proposed method is efficacious and generates solutions that are indistinguishable from the approx-
imate solutions generated by the RK4 method. Therefore, we can adapt the approach to various systems and develop results that are more accurate. On top of that, the new technique (ABC-FD) can identify chaotic situations. Consequently, this approach can be used to enhance the performance of other systems. In the future, this technique can be employed to determine the numerical solution for a multitude of models applicable in the fields of science and engineering.

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Published

2024-01-31

Issue

Section

Nonlinear Analysis

How to Cite

A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative. (2024). European Journal of Pure and Applied Mathematics, 17(1), 445-461. https://doi.org/10.29020/nybg.ejpam.v17i1.5043