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RESEARCH ARTICLE

New solitary wave solutions and modulation stability of the time-fractional coupled Konno-Oono model arising in a magnetic field

Hira Tariq1 ,  Hira Ashraf1 ,  Ghazala Akram2,3 ,  Hafiz Abdul Wajid4*
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1 Department of Mathematics, Government College Women University, Sialkot , Pakistan
2 Institute of Mathematics, University of the Punjab, Lahore , Pakistan
3 Department of Computer Engineering, Biruni University, Istanbul , Türkiye
4 Department of Electrical Engineering, Faculty of Engineering, Islamic University of Madinah, Madinah , Saudi Arabia
IJOCTA, 026250124 https://doi.org/10.36922/IJOCTA026250124
Received: 19 June 2026 | Revised: 9 July 2026 | Accepted: 14 July 2026 | Published online: 1 September 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

The time-fractional coupled Konno-Oono equation model describes a current-carrying rope placed in an outside magnetic field. This model is important for understanding wave behavior in such physical systems. However, finding a wide range or new soliton solutions of this model remains relatively unexplored. In this paper, we study this model using two analytical methods: the modified auxiliary equation method and the generalized projective Riccati equation method. The effects of different orders of time derivatives on the system are also examined using three types of derivatives: conformable, beta, and M-truncated. The proposed model yields many new solitary wave solutions, including periodic solitons, singular periodic shapes, dark-bright solitons, and anti-bell-shaped solutions. Unlike previous work, this study provides a broader family of solutions using simple and reliable methods. The physical behavior of these solutions is shown using 2D line graphs, 3D surface graphs, and contour plots generated with Wolfram Mathematica 9. We also discuss the stability of the proposed model. These results help us understand various natural and dynamical processes.

Keywords
Time-fractional coupled Konno-Oono equation
Generalized projective
Riccati equation method
Modified auxiliary equation method
Soliton solutions
Fractional derivatives
Modulation stability
Funding
None.
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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