Solitary wave solutions for the conformable time-fractional coupled Konno-Oono model via applications of three mathematical methods

Aly R. Seadawy; Asghar Ali; Taha Radwan; Wael W. Mohammed; Karim K. Ahmed; Aly R. Seadawy; Asghar Ali; Taha Radwan; Wael W. Mohammed; Karim K. Ahmed

doi:10.3934/math.2025718

AIMS Mathematics

2025, Volume 10, Issue 7: 16027-16044. doi: 10.3934/math.2025718

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Solitary wave solutions for the conformable time-fractional coupled Konno-Oono model via applications of three mathematical methods

1.
Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, 41411, Saudi Arabia
2.
Basic Sciences Research Center (BSRC), Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Mathematics, University of Education, Lahore, Multan Campus, Pakistan
4.
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
5.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
6.
Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt

Received: 01 June 2025 Revised: 22 June 2025 Accepted: 03 July 2025 Published: 16 July 2025
MSC : 35C05, 35C07, 35C08, 47J35

This research extensively investigates the solitary wave solutions of the fractional coupled Konno–Oono model, a prevalent framework in diverse scientific and engineering disciplines. Three mathematical methods called the simple equation method, the modified extended auxiliary equation mapping method, and the exponential-expansion method are gradually employed to derive the analytical solutions. Moreover, Mathematica 13.0 software is used to perform the analytical computations and graphical simulations. The explored outcomes have significant applications in the realm of magnetic fields. After the careful selection of parametric values under constrained conditions, some solutions are plotted in 2-dimensional and 3-dimensional spaces to understand the physical phenomena of the concerned model. Importantly, our findings affirm that the employed methods not only yield complete and uniform responses but also showcase simplicity, effectiveness, and remarkable computational efficiency. Hence, our research contributes valuable insights into the behavior of the fractional coupled Konno–Oono model, paving the way for enhanced comprehension and potential applications in magnetic field studies.
- fractional coupled Konno–Oono model (FCKOM),
- mathematical methods,
- soliton solutions,
- fractional derivatives
Citation: Aly R. Seadawy, Asghar Ali, Taha Radwan, Wael W. Mohammed, Karim K. Ahmed. Solitary wave solutions for the conformable time-fractional coupled Konno-Oono model via applications of three mathematical methods[J]. AIMS Mathematics, 2025, 10(7): 16027-16044. doi: 10.3934/math.2025718

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Abstract

This research extensively investigates the solitary wave solutions of the fractional coupled Konno–Oono model, a prevalent framework in diverse scientific and engineering disciplines. Three mathematical methods called the simple equation method, the modified extended auxiliary equation mapping method, and the exponential-expansion method are gradually employed to derive the analytical solutions. Moreover, Mathematica 13.0 software is used to perform the analytical computations and graphical simulations. The explored outcomes have significant applications in the realm of magnetic fields. After the careful selection of parametric values under constrained conditions, some solutions are plotted in 2-dimensional and 3-dimensional spaces to understand the physical phenomena of the concerned model. Importantly, our findings affirm that the employed methods not only yield complete and uniform responses but also showcase simplicity, effectiveness, and remarkable computational efficiency. Hence, our research contributes valuable insights into the behavior of the fractional coupled Konno–Oono model, paving the way for enhanced comprehension and potential applications in magnetic field studies.

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