Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction

• Published in: Complexity (New York, N.Y.) Vol. 2021; no. 1
• Main Authors: Alaoui, Mohammed Kbiri, Fayyaz, Rabia, Khan, Adnan, Shah, Rasool, Abdo, Mohammed S.
• Format: Journal Article
• Language: English
• Published: Hoboken Hindawi 2021; Hindawi Limited; Hindawi-Wiley
• Subjects: Approximation; Calculus; Decomposition; Engineering; Exact solutions; Graphs; Mathematicians; Methods; Partial differential equations; Perturbation methods; Polynomials
• ISSN: 1076-2787; 1099-0526
• DOI: 10.1155/2021/3248376

In this article, we find the solution of time-fractional Belousov–Zhabotinskii reaction by implementing two well-known analytical techniques. The proposed methods are the modified form of the Adomian decomposition method and homotopy perturbation method with Yang transform. In Caputo manner, the fractional derivative is used. The solution we obtained is in the form of series which helps in investigating the analytical solution of the time-fractional Belousov–Zhabotinskii (B-Z) system. To verify the accuracy of the proposed methods, an illustrative example is taken, and through graphs, the solution is shown. Also, the fractional-order and integer-order solutions are compared with the help of graphs which are easy to understand. It has been verified that the solution obtained by using the given approaches has the desired rate of convergence to the exact solution. The proposed technique’s principal benefit is the low amount of calculations required. It can also be used to solve fractional-order physical problems in a variety of domains.