THE TRAVELING WAVE SOLUTIONS OF THE CONFORMABLE TIME-FRACTIONAL ZOOMERON EQUATION BY USING THE MODIFIED EXPONENTIAL FUNCTION METHOD

Year 2024, Volume: 25 Issue: 1, 108 - 114, 28.03.2024

Aslı Alkan Tolga Aktürk Hasan Bulut

https://doi.org/10.18038/estubtda.1370631

Abstract

The present study focuses on the acquisition of traveling wave solutions associated with the conformable time-fractional Zoomeron equation through the utilization of the modified exponential function method (MEFM). The solution functions derived from mathematical computations encompass hyperbolic, trigonometric, and rational functions. Various graphical representations, such as 2D, 3D, contour graphs, and density graphs, are utilized to visually depict the distinct features of the solution functions derived from the determination of suitable parameters.

Keywords

The wave solution, Zoomeron equation, The conformable derivative

References

• Hossain AKS, Akbar MA. Closed form solutions of two nonlinear equation via the enhanced (G'/G) expansion method. Cogent Mathematics and Statistics, 2017, 4(1), 1355958.
• Akturk T, Bulut H, Gurefe Y. An application of the new function method to the Zhiber-Shabat equation. An International Journal of Optimization and Control: Theories & Applications, 2017, 7(3), 271-274.
• Baskonus HM, Bulut H. New hyperbolic function solutions for some nonlinear partial differential equation arising in mathematical physics. Entropy, 2015, 17(2015), 4255-4270.
• Chen Y, Yan Z. New exact solutions of (2+ 1)-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos, Solitons & Fractals, 2005, 26(2), 399-406.
• Dubrovsky VG, Lisitsyn YV. The construction of exact solutions of two-dimensional integrable generalizations of Kaup–Kuperschmidt and Sawada–Kotera equations via∂ ̄-dressing method. Physics Letters A, 2002, 295(4), 198-207.
• Mohiud-Din ST. Homotopy perturbation method for solving fourth-order boundary value problems, Math. Prob. Engr., 2007, 2007, 1-15. doi:10.1155/2007/98602.
• Baskonus HM, Bulut H, Atangana A. On the complex and hyperbolic structures of the longitudinal wave equation in a magneto-electro-elastic circular rod. Smart Materials and Structures, 2016, 25(3), 035022.
• Xu F. Application of Exp-function method to symmetric regularized long wave (SRLW) equation. Physics Letters A, 2008, 372(3), 252-257.
• Kumar D, Kaplan M. New analytical solutions of (2+1) dimensional conformable time-fractional Zoomeron equation via two distinct techniques,ChineseJ.Phys., 2018, 53, 2173-2185.
• Baskonus HM, Bulut H, Sulaiman TA. Investigation of various travelling wave solutions to the extended (2+1)-dimensional quantum ZK equation. The European Physical Journal Plus, 2017, 132(11), 482.
• Shen G, Sun Y, Xiong Y. New travelling-wave solutions for Dodd-Bullough equation. Journal of Applied Mathematics, 2013, 2013, 1-5.
• Naher H, Abdullah FA. New approach of (G′/G)-expansion method and new approach of generalized (G′/G)-expansion method for nonlinear evolution equation. American Institute of Physics Advances, 2013, 3(3), 032116.
• Gao W.,Rezazadeh H, Pinar Z, Baskonus HM, Sarwar, Yel G. Novel explicit solutions for the nonlinear Zoomeron equation by using newly extended direct algebraic technique. Optical and Quantum Electronics, 2020, 52, 1-13.
• Hosseini K, Korkmaz A, Bekir A, Samadani F, Zabihi A, Topsakal M. New wave form solutions of nonlinear conformable time-fractional Zoomeron equation in (2+ 1)-dimensions. Waves in Random and Complex Media, 2021, 31(2), 228-238.
• Demirbilek U, Ala V, Mamedov KR. Exact solutions of conformable time fractional Zoomeron equation via IBSEFM. Applied Mathematics-A Journal of Chinese Universities, 2021, 36, 554-563.