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Chaotic Behaviour, Sensitivity Assessment, and New Analytical Investigation to Find Novel Optical Soliton Solutions of M-Fractional Kuralay-II Equation

J. R. M. Borhan, E. I. Hassan, Arafa Dawood, Khaled Aldwoah (), Amani Idris A. Sayed, Ahmad Albaity and M. Mamun Miah ()
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J. R. M. Borhan: Department of Mathematics, Jashore University of Science and Technology, Jashore 7408, Bangladesh
E. I. Hassan: Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
Arafa Dawood: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Khaled Aldwoah: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
Amani Idris A. Sayed: Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia
Ahmad Albaity: Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia
M. Mamun Miah: Department of Mathematics, Khulna University of Engineering and Technology, Khulna 9203, Bangladesh

Mathematics, 2025, vol. 13, issue 13, 1-19

Abstract: The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and signal denoising, complex biological systems, optical fibers, plasma physics, population dynamics, and modern technology. These applications demonstrate the versatility and advantageousness of the stated model for complex systems in various scientific and engineering disciplines. One more essential objective of the present research is to find closed-form wave solutions of the assumed equation based on the ( G ′ G ′ + G + A ) -expansion approach. The results achieved are in exponential, rational, and trigonometric function forms. Our findings are more novel and also have an exclusive feature in comparison with the existing results. These discoveries substantially expand our understanding of nonlinear wave dynamics in various physical contexts in industry. By simply selecting suitable values of the parameters, three-dimensional (3 D ), contour, and two-dimensional (2 D ) illustrations are produced displaying the diagrammatic propagation of the constructed wave solutions that yield the singular periodic, anti-kink, kink, and singular kink-shape solitons. Future improvements to the model may also benefit from what has been obtained as well. The various assortments of solutions are provided by the described procedure. Finally, the framework proposed in this investigation addresses additional fractional nonlinear partial differential equations in mathematical physics and engineering with excellent reliability, quality of effectiveness, and ease of application.

Keywords: truncated M-fractional derivative; Kuralay-II equation; ( G ′ G ′ + G + A ) -expansion approach; solitons; chaotic; sensitivity; wave solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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