Exploring Solitons Solutions of a (3+1)-Dimensional Fractional mKdV-ZK Equation
Abstract
:1. Introduction
2. Methodology
Sr. No. | ||||
1 | 1 | or | ||
2 | ||||
3 | −1 | |||
4 | 1 | or | ||
5 | ||||
6 | −1 | |||
7 | 1 | |||
8 | 1 | |||
9 | 1 | |||
10 | 1 | |||
11 | or | |||
12 | ||||
13 | ||||
14 |
function | function | ||||
1 | 1 | ||||
1 | 1 | ||||
3. Implementation of the Expansion Method
4. Graphical Illustration and Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Hamza, A.E.; Osman, O.; Sarwar, M.U.; Aldwoah, K.; Saber, H.; Hleili, M. Exploring Solitons Solutions of a (3+1)-Dimensional Fractional mKdV-ZK Equation. Fractal Fract. 2024, 8, 498. https://doi.org/10.3390/fractalfract8090498
Hamza AE, Osman O, Sarwar MU, Aldwoah K, Saber H, Hleili M. Exploring Solitons Solutions of a (3+1)-Dimensional Fractional mKdV-ZK Equation. Fractal and Fractional. 2024; 8(9):498. https://doi.org/10.3390/fractalfract8090498
Chicago/Turabian StyleHamza, Amjad E., Osman Osman, Muhammad Umair Sarwar, Khaled Aldwoah, Hicham Saber, and Manel Hleili. 2024. "Exploring Solitons Solutions of a (3+1)-Dimensional Fractional mKdV-ZK Equation" Fractal and Fractional 8, no. 9: 498. https://doi.org/10.3390/fractalfract8090498