New exact solutions of the nonlinear space-time conformable symmetric regularized long wave equation using the extended fan sub-equation method
DOI:
https://doi.org/10.31349/RevMexFis.72.030702Keywords:
Nonlinear space-time conformable equations, Conformable derivative, Symmetric regularized long wave (SRLW), Exact solutionsAbstract
The non-linearity in numerous problems occurs due to the complexity of the given physical phenomena.
This work aims to present the extended Fan sub equation method,which is successfully applied to get the analytical solutions to the space-time conformable symmetric regularized long wave (SRLW) equation. The results may be useful for analysing the depth and spacing of parallel subsurface drains and long waves with small amplitudes on the water’s surface in channels. The results that are obtained of the proposed approach are highly accurate and give beneficial information on the actual dynamics of every problem. The recommended method may be extended to solve more significant fractional order problems due to its simple implementation.
Downloads
References
S. Rashid, R. Ashraf, and Z. Hammouch, New generalized fuzzy transform computations for solving fractional partial differential equations arising in oceanography, J. Ocean Eng. Sci. 8 (2023) 55-78 DOI: https://doi.org/10.1016/j.joes.2021.11.004
A.M. Selvam, Nonlinear dynamics and chaos: applications in meteorology and atmospheric physics, in: Self-organized Criticality and Predictability in Atmospheric Flows, (Springer, 2017), pp. 1-40 DOI: https://doi.org/10.1007/978-3-319-54546-2_1
R. Steijl, Quantum algorithms for nonlinear equations in fluid mechanics, in: Quantum Computing and Communications, (IntechOpen, 2020) DOI: https://doi.org/10.5772/intechopen.86685
Y. Brenier, Some geometric PDEs related to hydrodynamics and electrodynamics, arXiv:math/0305009 (2003)
S.A. Gourley, J.W.-H. So, and J.H. Wu, Nonlocality of reactiondiffusion equations induced by delay: biological modeling and nonlinear dynamics, J. Math. Sci. 124 (2004) 5119-5153 DOI: https://doi.org/10.1023/B:JOTH.0000047249.39572.6d
C.E. Seyler and D.L. Fenstermacher, A symmetric regularizedlong-wave equation, Phys. Fluids 27 (1984) 4-7 DOI: https://doi.org/10.1063/1.864487
Ö. Güner et al., Exact solutions of the space time fractional symmetric regularized long wave equation using different methods, Adv. Math. Phys. 2014 (2014) DOI: https://doi.org/10.1155/2014/456804
M. Shakeel and S.T. Mohyud-Din, A novel (G’/G)-expansion method and its application to the space-time fractional symmetric regularized long wave (SRLW) equation, Adv. Trends Math. 2 (2015) DOI: https://doi.org/10.18052/www.scipress.com/ATMath.2.1
Ö. Güner and A. Bekir, Solving nonlinear space-time fractional differential equations via ansatz method, Comput. Methods Differ. Equ. 6 (2018) 1-11
D. Yaro, A.R. Seadawy, D. Lu, W.O. Apeanti, and S.W. Akuamoah, Dispersive wave solutions of the nonlinear fractional Zakhorov-Kuznetsov-Benjamin-Bona-Mahony equation and fractional symmetric regularized long wave equation, Results Phys. 12 (2019) 1971-1979 DOI: https://doi.org/10.1016/j.rinp.2019.02.005
M.A. Khan, M.A. Akbar, and N.N. binti Abd Hamid, Traveling wave solutions for space-time fractional Cahn Hilliard equation and space-time fractional symmetric regularized longwave equation, Alexandria Eng. J. 60 (2021) 1317-1324 DOI: https://doi.org/10.1016/j.aej.2020.10.053
N. Maarouf, H. Maadan, and K. Hilal, Lie symmetry analysis and explicit solutions for the time-fractional regularized longwave equation, Int. J. Differ. Equ. 2021 (2021) 1-11 DOI: https://doi.org/10.1155/2021/6614231
S.Ç. Ünal, A. Daşcıoǧlu, and D.V. Bayram, Jacobi elliptic function solutions of space-time fractional symmetric regularized long wave equation, Math. Sci. Appl. E-Notes 9 (2021) 53-63 DOI: https://doi.org/10.36753/mathenot.688493
Q. Zhu and J. Qi, Exact solutions of the nonlinear space-time fractional partial differential symmetric regularized long wave (SRLW) equation by employing two methods, Adv. Math. Phys. 2022 (2022) 8062119 DOI: https://doi.org/10.1155/2022/8062119
J. Gao, S. He, Q. Bai, and J. Liu, A time two-mesh finite difference numerical scheme for the symmetric regularized long wave equation, Fractal Fract. 7 (2023) 487 DOI: https://doi.org/10.3390/fractalfract7060487
J. Zhang, Z. Zheng, H. Meng, and Z. Wang, Bifurcation analysis and exact solutions of the conformable time fractional symmetric regularized long wave equation, Chaos Solitons Fractals 190 (2025) 115744 DOI: https://doi.org/10.1016/j.chaos.2024.115744
K. Aldwoah, N. Eljaneid, B. Younis, M. Alsharafi, O. Osman, and B. Muflh, Analytical solutions of the time-fractional symmetric regularized long wave equation using the model expansion method, Sci. Rep. 15 (2025) 16232 DOI: https://doi.org/10.1038/s41598-025-00240-x
R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014) 65-70 DOI: https://doi.org/10.1016/j.cam.2014.01.002
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015) 57-66 DOI: https://doi.org/10.1016/j.cam.2014.10.016
A. Atangana, D. Baleanu, and A. Alsaedi, New properties of conformable derivative, Open Math. 13 (2015) 1-10 DOI: https://doi.org/10.1515/math-2015-0081
S.M. Ege and E. Misirli, The modified Kudryashov method for solving some fractional-order nonlinear equations, Adv. Differ. Equ. 2014 (2014) 1-13 DOI: https://doi.org/10.1186/1687-1847-2014-135
Y. Gurefe, The generalized Kudryashov method for the nonlinear fractional partial differential equations with the betaderivative, Rev. Mex. Fis. 66 (2020) 771-781 DOI: https://doi.org/10.31349/RevMexFis.66.771
A.K. Alsharidi and A. Bekir, Discovery of new exact wave solutions to the M-fractional complex three coupled Maccari’s system by Sardar sub-equation scheme, Symmetry 15 (2023) 1567 DOI: https://doi.org/10.3390/sym15081567
D. Chou, H. Ur Rehman, A. Amer, and A. Amer, New solitary wave solutions of generalized fractional Tzitzéica-type evolution equations using Sardar sub-equation method, Opt. Quantum Electron. 55 (2023) 1-16 DOI: https://doi.org/10.1007/s11082-023-05425-0
H. Rehman, A. Amer, and A. Amer, New solitary wave solutions of generalized fractional Tzitzéica-type evolution equations using Sardar sub-equation method (2023) DOI: https://doi.org/10.21203/rs.3.rs-3210751/v1
R. Ashraf, R. Nawaz, O. Alabdali, N. Fewster-Young, A.H. Ali, F. Ghanim, and A. Alb Lupas, A new hybrid optimal auxiliary function method for approximate solutions of non-linear fractional partial differential equations, Fractal Fract. 7 (2023) 673 DOI: https://doi.org/10.3390/fractalfract7090673
G. Akram, M. Sadaf, I. Zainab, M. Abbas, and A. Akgül, A comparative study of time fractional nonlinear Drinfeld-Sokolov-Wilson system via modified auxiliary equation method, Fractal Fract. 7 (2023) 665 DOI: https://doi.org/10.3390/fractalfract7090665
A. Aslan, Exact solutions for fractional DDEs via auxiliary equation method coupled with the fractional complex transform, Math. Methods Appl. Sci. 39 (2016) 5619-5625 DOI: https://doi.org/10.1002/mma.3946
D. Abbas and A. Kadem, Application of the extended Fan subequation method to time fractional Burgers-Fisher equation, Tatra Mt. Math. Publ. 79 (2021) 1-12 DOI: https://doi.org/10.2478/tmmp-2021-0016
E. Fendzi-Donfack and A. Kenfack-Jiotsa, Extended Fan’s subODE technique and its application to a fractional nonlinear coupled network including multicomponents-LC blocks, Chaos Solitons Fractals 177 (2023) 114266 DOI: https://doi.org/10.1016/j.chaos.2023.114266
M. Djilali and A. Hakem, (G’/G)-expansion method to seek traveling wave solutions for some fractional nonlinear PDEs arising in natural sciences, Adv. Theory Nonlinear Anal. Appl. 7 (2023) 303-318 DOI: https://doi.org/10.31197/atnaa.1125691
S. Biswas, U. Ghosh, and S. Raut, Construction of fractional granular model and bright, dark, lump, breather types soliton solutions using Hirota bilinear method, Chaos Solitons Fractals 172 (2023) 113520 DOI: https://doi.org/10.1016/j.chaos.2023.113520
H.-M. Zhu, J. Zheng, and Z.-Y. Zhang, Approximate symmetry of time-fractional partial differential equations with a small parameter, Commun. Nonlinear Sci. Numer. Simul. 125 (2023) 107404 DOI: https://doi.org/10.1016/j.cnsns.2023.107404
R. Sahadevan and P. Prakash, On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations, Chaos Solitons Fractals 104 (2017) 107- 120 DOI: https://doi.org/10.1016/j.chaos.2017.07.019
O. Tasbozan, Y. C¸ enesiz, A. Kurt, and D. Baleanu, New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method, Open Phys. 15 (2017) 647-651 DOI: https://doi.org/10.1515/phys-2017-0075
S. Ramya, K. Krishnakumar, and R. Ilangovane, Exact solutions of time fractional generalized Burgers-Fisher equation using exp and exponential rational function methods, Int. J. Dyn. Control (2023) 1-11 DOI: https://doi.org/10.1007/s40435-023-01267-6
A. Singh and S. Pippal, Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM), Int. J. Math. Ind. (2023) DOI: https://doi.org/10.1142/S2661335223500119
D. Albogami, D. Maturi, and H. Alshehri, Adomian decomposition method for solving fractional time-Klein-Gordon equations using Maple, Appl. Math. 14 (2023) 411-418 DOI: https://doi.org/10.4236/am.2023.146024
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 R. Hussain, A. Ilyas, H. Rezazadeh, M. Ali Hosseinzadeh, S. Salahshour
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
