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Soliton Solutions of Nonlinear Fractional Differential Fquations via Functional Variable Method

by Patanjali Sharma
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 187 - Number 24
Year of Publication: 2025
Authors: Patanjali Sharma
10.5120/ijca2025925393

Patanjali Sharma . Soliton Solutions of Nonlinear Fractional Differential Fquations via Functional Variable Method. International Journal of Computer Applications. 187, 24 ( Jul 2025), 39-45. DOI=10.5120/ijca2025925393

@article{ 10.5120/ijca2025925393,
author = { Patanjali Sharma },
title = { Soliton Solutions of Nonlinear Fractional Differential Fquations via Functional Variable Method },
journal = { International Journal of Computer Applications },
issue_date = { Jul 2025 },
volume = { 187 },
number = { 24 },
month = { Jul },
year = { 2025 },
issn = { 0975-8887 },
pages = { 39-45 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume187/number24/soliton-solutions-of-nonlinear-fractional-differential-equations-via-functional-variable-method/ },
doi = { 10.5120/ijca2025925393 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2025-07-31T02:39:55.951874+05:30
%A Patanjali Sharma
%T Soliton Solutions of Nonlinear Fractional Differential Fquations via Functional Variable Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 187
%N 24
%P 39-45
%D 2025
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, the functional variable method is utilized to derive analytical solutions for the (2 + 1)-dimensional time-fractional Zoomeron equation and the space-time fractional modified regularized long-wave equation, based on the Jumarie’s modified Riemann-Liouville derivative. The given equations are transformed into nonlinear ordinary differential equations of integer order, which are then solved using the proposed functional variable method, a novel analytical approach. Consequently, several exact solutions are successfully obtained. The results demonstrate that the proposed method is both efficient and easy to implement.

References
  1. A. A. Mamun, S. N. Ananna, T. An, N. H. M. Shahen, M. Asaduzzaman Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics Heliyon 7(8) (2021) e07704.
  2. S. Sirisubtawee, S. Koonprasert, S. Sungnul, T. Leekparn Exact traveling wave solutions of the space-time fractional complex Ginzburg-Landau equation and the space-time fractional Phi-four equation using reliable methods Adv. Diff. Equ. 2019 (2019) 219.
  3. R. Shah, Y. Alkhezi, K. Alhamad An analytical approach to solve the fractional Benney equation using the q-homotopy analysis transform method Symmetry 15(3) (2023) 669 .
  4. U. Ali, H. Ahmad, J. Baili, T. Botmart, M.A. Aldahlan Exact analytical wave solutions for space-time variable-order fractional modified equal width equation Results Phys. 33 (2022) 105216
  5. U. Zaman, M.A. Arefin, M.A. Akbar, M.H. Uddin Solitary wave solution to the space-time fractional modified equal width equation in plasma and optical fiber systems Results Phys. 52 (2023) 106903
  6. K. Raslan, K.K. Ali, M.A. Shallal The modified extended tanh method with the Riccati equation for solving the space-time fractional ew and mew equations Chaos Solitons Fract. 103 (2017) 404?409
  7. M.A. Khatun, M.A. Arefin, M.A. Akbar, M.H. Uddin Numerous explicit soliton solutions to the fractional simplified Camassa-Holm equation through two reliable techniques Ain Shams Eng. J. 14 (2023), 102214.
  8. H M Baskonus New acoustic wave behaviors to the Davey- Stewartson equation with power-law nonlinearity arising in fluid dynamics Nonlinear Dyn 86 (2016) 77?83.
  9. K R Raslan The first integral method for solving some important nonlinear partial differential equations Nonlinear Dyn 53(4) (2008) 959?979.
  10. P Sharma, O Y Kushel The First Integral Method for Huxley Equation International Journal of Nonlinear Science 10(1) (2010) 46-52.
  11. S T Demiray, Y Pandir, H Bulut All exact travelling wave solutions of Hirota equation and Hirota-Maccari system Optik 127(4) (2016) 1848?1859.
  12. M Kaplan, A Bekir, M N Ozer Solving nonlinear evolution equation system using two different methods Open Phys 13 (2015) 383?388.
  13. H M Baskonus New acoustic wave behaviors to the Davey- Stewartson equation with power-law nonlinearity arising in fluid dynamics Nonlinear Dyn 86 (2016) 77?83.
  14. M A Akbar, N M Ali The improved F-expansion method with Riccati equation and its application in mathematical physics Cogent Math Stat 41 (2017) 282?577.
  15. M A Kayum, S Ara, H K Barman, M A Akbar Soliton solutions to voltage analysis in nonlinear electrical transmission lines and electric signals in telegraph lines Results Phys 18 (2020) 103269.
  16. MA Kayum,MA Akbar,MS Osman Competent closed form soliton solutions to the nonlinear transmission and the low pass electrical transmission lines Eur Phys J Plus 135 (2020) 575.
  17. M E Islam, H K Barman, M A Akbar Search for interactions of phenomena described by the coupled Higgs field equations through analytical solutions Opt Quant Electron 52 (2020) 468.
  18. W Y Guan, B Q Li Mixed structures of optical breather and rogue wave for a variable coefficient inhomogeneous fiber system Opt Quant Electron 51 (2019) 352.
  19. Y L Ma Interaction and energy transition between the breather and rogue wave for a generalized nonlinear Schrodinger system with two higher-order dispersion operators in optical fibers Nonlinear Dyn 97 (2019) 95?105.
  20. B Q Li, Y L Ma Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrodinger equation Appl Math Comput 386 (2020) 125469.
  21. F. Meng, Q. Feng Exact solutions with variable coefficient function forms for conformable fractional partial differential equations by an auxiliary equation method Advances in Mathematical Physics vol. 2018, Article ID 4596506, 8 pages, 2018.
  22. S. T. Demiray, S. Duman MTEM to the (2+1)-dimensional ZK equation and Chafee-Infante equation Advanced Mathematical Models and Applications 6(1) (2021) 63?70.
  23. A Zerarka, S Ouamane, A Attaf On the functional variable method for finding exact solutions to a class of wave equations, Appl. Math. and Comput. 217 (2010) 2897-2904
  24. A Zerarka, S Ouamane Application of the functional variable method to a class of nonlinear wave equations, World Journal of Modelling and Simulation, 6(2) (2010) 150-160
  25. B Babajanov, F Abdikarimov The Application of the Functional Variable Method for Solving the Loaded Non-linear Evaluation Equations, Frontiers in Applied Mathematics and Statistics, 6 (2022) 912674
  26. B Babajanov, F Abdikarimov Soliton and PeriodicWave Solutions of the Nonlinear Loaded (3+1)-Dimensional Version of the Benjamin-Ono Equation by Functional Variable Method, Journal of Nonlinear Modeling and Analysis, 5(4) (2023) 782?789
  27. B Babajanov, F Abdikarimov New soliton solutions of the Burgers equation with additional time-dependent variable coefficient, WSEAS TRANSACTIONS on FLUID MECHANICS, 19 (2024) 59-63
  28. G. Jumarie Modified Riemann?Liouville derivative and fractional Taylor series of nondifferentiable functions further results Comput. Math. Appl. 51 (2006) 1367?1376.
  29. G. Jumarie Table of some basic fractional calculus formulae derived from a modified Riemann?Liouvillie derivative for non differentiable functions, Appl. Math. Lett. 22 (2009) 378?385.
  30. B Lu The first integral method for some time fractional differential equations J. Math. Anal. Appl. 395(2) (2012) 684-693.
  31. A Zerarka, S Ouamane and A Attaf On the functional variable method for finding exact solutions to a class of wave equations Appl. Math. Comput. 217(7) (2010) 2897-2904
  32. E. Tala-Tebue, Z.I. Djoufack, A. Djimeli-Tsajio, A. Kenfack- Jiotsa Solitons and other solutions of the nonlinear fractional Zoomeron equation Chin. J. Phys. 56(3) (2018) 1232?1246.
  33. F. Calogero, A. Degasperis Nonlinear evolution equations solvable by the inverse spectral transform I. II Nuovo Cimento B 32 (1976) 201?242.
  34. M. Kaplan, A. Bekir, M.N. Ozer A simple technique for constructing exact solutions to nonlinear differential equations with conformable fractional derivative, Opt. Quant. Electron. 49 (8) (2017) 266.
  35. A. Akbulut, M. Kaplan Auxiliary equation method for timefractional differential equations with conformable derivative, Comput. Math. Appl. 75 (3) (2018) 876?882.
  36. E. Aksoy, A.C. vikel, A. Bekir Soliton solutions of (2+1)- dimensional time-fractional Zoomeron equation, Optik 127 (17) (2016) 6933?6942.
  37. O. Guner, A. Bekir Bright and dark soliton solutions for some nonlinear fractional differential equations, Chin. Phys. B 25 (3) (2016) 030203.
  38. F Batool, G Akram,M Sadaf, U Mehmood Dynamics Investigation and Solitons Formation for (2+1)-Dimensional Zoomeron Equation and Foam Drainage Equation Journal of Nonlinear Mathematical Physics 30 (2023) 628?645.
  39. M Alshammari, K Moaddy, M Naeem, Z Alsheekhhussain et al. Solitary and PeriodicWave Solutions of Fractional Zoomeron Equation fractal and fractional 8(4) (2024) 222.
  40. S Hossain, M.M. Roshid, M Uddin et al. Abundant timewavering solutions of a modified regularized long wave model using the EMSE technique Partial Differential Equations in Applied Mathematics 8 (2023) 100551.
  41. D.H. Peregrine Calculations of the development of an undular bore J Fluid Mech 25(2) (1966) 321-330.
Index Terms

Computer Science
Information Sciences

Keywords

(2 + 1)-dimensional time-fractional Zoomeron equation fractional modified regularized long-wave equation Jumarie’s modified Riemann-Liouville derivative Functional Variable Method

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