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Keywords = Fractional Belousov–Zhabotinsky equation

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11 pages, 1198 KiB  
Article
Optimal Auxiliary Function Method for Analyzing Nonlinear System of Belousov–Zhabotinsky Equation with Caputo Operator
by Azzh Saad Alshehry, Humaira Yasmin, Muhammad Wakeel Ahmad, Asfandyar Khan and Rasool Shah
Axioms 2023, 12(9), 825; https://doi.org/10.3390/axioms12090825 - 28 Aug 2023
Cited by 4 | Viewed by 1465
Abstract
This paper introduces the optimal auxiliary function method (OAFM) for solving a nonlinear system of Belousov–Zhabotinsky equations. The system is characterized by its complex dynamics and is treated using the Caputo operator and concepts from fractional calculus. The OAFM provides a systematic approach [...] Read more.
This paper introduces the optimal auxiliary function method (OAFM) for solving a nonlinear system of Belousov–Zhabotinsky equations. The system is characterized by its complex dynamics and is treated using the Caputo operator and concepts from fractional calculus. The OAFM provides a systematic approach to obtain approximate analytical solutions by constructing an auxiliary function. By optimizing the parameters of the auxiliary function, an approximate solution is derived that closely matches the behavior of the original system. The effectiveness and accuracy of the OAFM are demonstrated through numerical simulations and comparisons with existing methods. Fractional calculus enhances the understanding and modeling of the nonlinear dynamics in the Belousov–Zhabotinsky system. This study contributes to fractional calculus and nonlinear dynamics, offering a powerful tool for analyzing and solving complex systems such as the Belousov–Zhabotinsky equation. Full article
(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inequalities)
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11 pages, 733 KiB  
Article
Numerical Analysis of the Fractional-Order Belousov–Zhabotinsky System
by Humaira Yasmin, Azzh Saad Alshehry, Asfandyar Khan, Rasool Shah and Kamsing Nonlaopon
Symmetry 2023, 15(4), 834; https://doi.org/10.3390/sym15040834 - 30 Mar 2023
Cited by 6 | Viewed by 1688
Abstract
This paper presents a new approach for finding analytic solutions to the Belousov–Zhabotinsky system by combining the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) with the Elzaki transform. The ADM and HPM are both powerful techniques for solving nonlinear differential [...] Read more.
This paper presents a new approach for finding analytic solutions to the Belousov–Zhabotinsky system by combining the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) with the Elzaki transform. The ADM and HPM are both powerful techniques for solving nonlinear differential equations, and their combination allows for a more efficient and accurate solution. The Elzaki transform, on the other hand, is a mathematical tool that transforms the system into a simpler form, making it easier to solve. The proposed method is applied to the Belousov–Zhabotinsky system, which is a well-known model for studying nonlinear chemical reactions. The results show that the combined method is capable of providing accurate analytic solutions to the system. Furthermore, the method is also able to capture the complex behavior of the system, such as the formation of oscillatory patterns. Overall, the proposed method offers a promising approach for solving complex nonlinear differential equations, such as those encountered in the field of chemical kinetics. The combination of ADM, HPM, and the Elzaki transform allows for a more efficient and accurate solution, which can provide valuable insights into the behavior of nonlinear systems. Full article
(This article belongs to the Section Mathematics)
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