Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes
Zafar A. Raheel M. Ali M.R. Myrzakulova Z. Bekir A. Myrzakulov R.
October 2023Multidisciplinary Digital Publishing Institute (MDPI)
Symmetry
2023#15Issue 10
This article concerns new analytical wave solutions of the Kuralay-II equations (K-IIAE and K-IIBE) with exploration of a new definition of the derivative. This model is used in various fields, like nonlinear optics, ferromagnetic materials and optical fibers. For this purpose, the (Formula presented.) function, the extended sinh-Gordon equation expansion scheme, and the generalized Kudryashov schemes were utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular and other kinds of solitons. These results are obtained and also verified by the Mathematica tool. Some of the solutions are explained with 2-D, 3-D and contour plots using the Mathematica tool. The solutions obtained succede the present solutions in the literature. For the first time, the effect of the fractional derivative on the solutions is also shown graphically for this model. The analytical wave solutions are highly desirable as they offer insights into the underlying physics or mathematics of a system and provide a framework for further analysis. The results obtained can also be fruitful for the development of models in the future. The schemes used in this research are effective, easy to apply, and reliably handle other fractional non-linear partial differential equations.
expa function scheme , extended sinh-Gordon equation expansion scheme , generalized Kudryashov scheme , new analytical wave solutions , space-time fractional Kuralay-II equations
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Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, 61120, Pakistan
Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Egypt
Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha, 13518, Egypt
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana, 010000, Kazakhstan
Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, Eskisehir, 26030, Turkey
Department of Mathematics
Faculty of Engineering and Technology
Basic Engineering Science Department
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics
Neighbourhood of Akcaglan
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