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Keywords = fractional-order Belousov–Zhabotinsky system

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15 pages, 1108 KiB  
Article
A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System
by Samir A. El-Tantawy, Rasool Shah, Albandari W. Alrowaily, Nehad Ali Shah, Jae Dong Chung and Sherif. M. E. Ismaeel
Mathematics 2023, 11(7), 1751; https://doi.org/10.3390/math11071751 - 6 Apr 2023
Cited by 10 | Viewed by 1789
Abstract
In this article, we present a modified strategy that combines the residual power series method with the Laplace transformation and a novel iterative technique for generating a series solution to the fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use the Laurent series [...] Read more.
In this article, we present a modified strategy that combines the residual power series method with the Laplace transformation and a novel iterative technique for generating a series solution to the fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use the Laurent series in their development. The new procedures’ advantages include the accuracy and speed in obtaining exact/approximate solutions. The suggested approach examines the fractional nonlinear BZ system that describes flow motion in a pipe. Full article
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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 1687
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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