Have a personal or library account? Click to login
A new modified conformal expansion method to some nonlinear conformal partial differential equations Cover

A new modified conformal expansion method to some nonlinear conformal partial differential equations

Open Access
|Dec 2025

References

  1. Khalique C.M., Plaatjie K., Symmetry methods and conservation laws for the nonlinear generalized 2D equal-width partial differential equation of engineering, Mathematics, 10(1), 24, 2021.
  2. Patsiuk O., Kovalenko S., Symmetry reduction and exact solutions of the non-linear Black-Scholes equation, Communications in Nonlinear Science and Numerical Simulation, 62, 164–173, 2018.
  3. Mahak N., Akram G., Exact solitary wave solutions of the (1+1)-dimensional Fokas-Lenells equation, Optik, 208(164459), 1–9, 2020.
  4. Kalita J., Das R., Hosseini K., Salahshour S., Baleanu D., Some models in unmagnetized plasma involving kaniadakis distributed electrons and temperature ratio: Dust ion acoustic solitary waves, Journal of Applied and Computational Mechanics, 10(4), 792–800, 2024.
  5. Gasmi B., Moussa A.A., Mati Y., Alhakim L.A., Akgül A., New exact traveling wave solutions to the Kawahara equation using the tanh(ξ) expansion method, International Journal of Applied and Computational Mathematics, 9(5), 98, 2023.
  6. [6] Bashir M.A., Moussa A.A., New approach of GG \left({{{G'} \over G}} \right) expansion method applications to KdV equation, Journal of Mathematics Research, 6(1), 24–31, 2014.
    BashirM.A. MoussaA.A. New approach of GG \left({{{G'} \over G}} \right) expansion method applications to KdV equation Journal of Mathematics Research 6 1 24 31 2014
  7. Zayed E.M.E., Nowehy A.G., New extended auxiliary equation method for finding many new jacobi elliptic function solutions of three nonlinear Schrödinger equations, Waves in Random and Complex Media, 27(3), 420–439, 2017.
  8. Jazmati M.S., Analytical solutions of some nonlinear space-time fractional differential equations via improved Expfunction method, Journal of Qassim University for Science, 9(1), 1–16, 2016.
  9. Alhakim L.A., Moussa A.A., The double auxiliary equations method and its application to space-time fractional non-linear equations, Journal of Ocean Engineering and Science, 4(1), 7–13, 2019.
  10. Gasmi B., Alhakim L., Mati Y., Moussa A., Akgül A., Wannan R., Asad J., Novel exact and solitary wave solutions for the time-fractional nonlinear Maccari's system, Contemporary Mathematics, 4(4), 937–950, 2023.
  11. Bashir M.A., Moussa A.A., Alhakim L.A., The new generalized of exp(−ϕ(ξ)) expansion method and its application to some complex nonlinear partial differential equation, Journal of Advanced in Mathematics, 9(8), 2905–2926, 2015.
  12. Bashir M.A., Moussa A.A., The cotha (ξ)expansion method and its application to the Davey-Stewartson equation, Applied Mathematical Sciences, 8(78), 3851–3868, 2014.
  13. Gasmi B., Moussa A., Mati Y., Alhakim L., Baskonus H.M., Bifurcation and exact traveling wave solutions to a conformable nonlinear Schrödinger equation using a generalized double auxiliary equation method, Optical and Quantum Electronics, 56(18), 1–16, 2024.
  14. Gasmi B., Ciancio A., Moussa A., Alhakim L., Mati Y., New analytical solutions and modulation instability analysis for the nonlinear (1+1)-dimensional Phi-four model, International Journal of Mathematics and Computer in Engineering, 1(1), 79–90, 2023.
  15. Gasmi B., Kessi A., Jarad F., Hammouch Z., Various optical solitons to the (1+1)-Telegraph equation with space-time conformable derivatives, International Journal of Nonlinear Analysis and Applications, 12, 767–780, 2021.
  16. Bashir M., Hakim L.A., New F expansion method and its applications to modified KdV equation, Journal of Mathematics Research, 5(4), 38–94, 2013.
  17. Chen H., Zhang H., Improved jacobin elliptic method and its applications, Chaos Solitons and Fractals, 15(3), 585–591, 2003.
  18. Gasmi B., Moussa A., Mati Y., Alhakim L., Akgül A., Solving nonlinear partial differential equations using a novel Cham method, Journal of Taibah University for Science, 17(1), 2272728, 2023.
  19. Gasmi B., Alhakim L., Mati Y., Moussa A., Baskonus H.M., New analytical solutions to the nonlinear Schrödinger equation via an improved Cham method in conformable operator, Modern Physics Letters B, 38(33), 2450327, 2024.
  20. Moussa A.A., Alhakim L.A., Conformal fractional ((D_ξ^ α G (ξ))/G (ξ))-expansion method and its applications for solving the nonlinear fractional Sharma-Tasso-Olver equation, European Journal of Mathematics and Statistics, 2(5), 1–8, 2021.
  21. He J.H., Wu X.H., Exp-function method for nonlinear wave equations, Chaos Solitons and Fractals, 30(3), 700–708, 2006.
  22. Sirendaoreji, Auxiliary equation method and new solutions of Klein-Gordon equations, Chaos Solitons and Fractals, 31(4), 943–950, 2007.
  23. Zayed E.M.E., Alurrfi K.A.E., Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrödinger-type equations, Applied Mathematics and Computation, 289, 111–131, 2016.
  24. Zhang S., Zhang H.Q., Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A, 375(7), 1069–1073, 2011.
  25. Zhang G.Y., Feng Q., Fractional Riccati equation rational expansion method for fractional differential equations, Applied Mathematics and Information Sciences: An International Journal, 7(4), 1575–1584, 2013.
  26. Javeed S., Hncal E., Solving coupled non-linear higher order BVPs using improved shooting method, International Journal of Mathematics and Computer in Engineering, 2(2), 165–178, 2024.
  27. Hosseini K., Alizadeh F., Sadri K., Hinçal E., Akbulut A., Alshehri H.M., Osman M.S., Lie vector fields, conservation laws, bifurcation analysis, and Jacobi elliptic solutions to the Zakharov–Kuznetsov modified equal-width equation, Optical and Quantum Electronics, 56(506), 1–19, 2024.
  28. Hosseini K., Alizadeh F., Hinçal E., Baleanu D., Akgül A., Hassan A.M., Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation, Results in Physics, 54, 107129, 2023.
  29. Hosseini K., Hinçal E., Ilie M., Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a generalized Schrödinger equation, Nonlinear Dynamics, 111, 17455–17462, 2023.
  30. Hosseini K., Alizadeh F., Hinçal E., Kaymakamzade B., Dehingia K., Osman M.S., A generalized nonlinear Schrödinger equation with logarithmic nonlinearity and its Gaussian solitary wave, Optical and Quantum Electronics, 56(929), 1–9, 2024.
  31. Whitham G.B., Variational methods and applications to water waves, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 299(1456), 6–25, 1967.
  32. Esipov S.E., Coupled Burgers equations: A model of polydispersive sedimentation, Physical Review E, 52(4), 3711–3718, 1995.
  33. Zhao J., Tang B., Kumar S., Hou Y., The extended fractional sub-equation method for nonlinear fractional differential equations, Mathematical Problems in Engineering, 2012(924956), 1–11, 2012.
  34. Katugampola U.N., A new fractional derivative with classical properties, arXiv:1410.6535, 2014.
Language: English
Submitted on: May 31, 2024
Accepted on: Sep 3, 2024
Published on: Dec 17, 2025
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2025 Lama Alhakim, Alaaeddin Moussa, Boubekeur Gasmi, Yazid Mati, Md Nurul Raihen, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

AHEAD OF PRINT