Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction
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 fra...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/3248376 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832545999743090688 |
|---|---|
| author | Mohammed Kbiri Alaoui Rabia Fayyaz Adnan Khan Rasool Shah Mohammed S. Abdo |
| author_facet | Mohammed Kbiri Alaoui Rabia Fayyaz Adnan Khan Rasool Shah Mohammed S. Abdo |
| author_sort | Mohammed Kbiri Alaoui |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-876bd6ec513e475799bd8f92bed9e4b5 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-876bd6ec513e475799bd8f92bed9e4b52025-02-03T07:24:13ZengWileyComplexity1099-05262021-01-01202110.1155/2021/3248376Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky ReactionMohammed Kbiri Alaoui0Rabia Fayyaz1Adnan Khan2Rasool Shah3Mohammed S. Abdo4Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn 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.http://dx.doi.org/10.1155/2021/3248376 |
| spellingShingle | Mohammed Kbiri Alaoui Rabia Fayyaz Adnan Khan Rasool Shah Mohammed S. Abdo Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction Complexity |
| title | Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction |
| title_full | Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction |
| title_fullStr | Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction |
| title_full_unstemmed | Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction |
| title_short | Analytical Investigation of Noyes–Field Model for Time-Fractional Belousov–Zhabotinsky Reaction |
| title_sort | analytical investigation of noyes field model for time fractional belousov zhabotinsky reaction |
| url | http://dx.doi.org/10.1155/2021/3248376 |
| work_keys_str_mv | AT mohammedkbirialaoui analyticalinvestigationofnoyesfieldmodelfortimefractionalbelousovzhabotinskyreaction AT rabiafayyaz analyticalinvestigationofnoyesfieldmodelfortimefractionalbelousovzhabotinskyreaction AT adnankhan analyticalinvestigationofnoyesfieldmodelfortimefractionalbelousovzhabotinskyreaction AT rasoolshah analyticalinvestigationofnoyesfieldmodelfortimefractionalbelousovzhabotinskyreaction AT mohammedsabdo analyticalinvestigationofnoyesfieldmodelfortimefractionalbelousovzhabotinskyreaction |