International Scientific Journal

Authors of this Paper

External Links


In this paper, we mainly consider the local fractional Vakhnenko-Parkes equation with the local fractional derivative for the first time. Some new soliton solutions of local fractional Vakhnenko-Parkes equation are derived by using local fractional wave method. These obtained soliton solutions suggest that this proposed approach is effective, simple and reliable. Finally, the physical characteristics of these new soliton solutions are described through 3-D figures.
PAPER REVISED: 2023-05-13
PAPER ACCEPTED: 2023-06-10
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 5, PAGES [3877 - 3882]
  1. Wazwaz, A. M., Solitons of the (2+1)-Dimensional and the (3+1)-Dimensional Logarithmic Boussinesq Equations, International Journal of Numerical Methods for Heat & Fluid Flow, 26 (2016), 6, pp. 1699-1709
  2. Yang, X. J., et al., A New Computational Approach for Solving Nonlinear Local Fractional PDEs, Journal of Computational and Applied Mathematics, 339 (2018), Sept., pp. 285-296
  3. X.-J. Yang, et al., A New Insight into Complexity From the Local Fractional Calculus View Point: Modelling Growths of Populations, Mathematical Methods in the Applied Sciences, 40 (2017), 17, pp. 6070-6132
  4. Zhou, Q., et al., Optical Solitons in Photonic Crystal Fibers with Spatially Inhomogeneous Nonlinearities, Optoelectronics and Advanced Materials-Rapid Communications, 8 (2014), Nov., pp. 995-997
  5. Cevikel, A. C., et al., Construction of Periodic and Solitary Wave Solutions for the Complex Nonlinear Evolution Equations, Journal of The Franklin Institute, 2 (2014), 2, pp. 694-700
  6. Tripathy, A., et al., New Optical Soliton Solutions of Biswas-Arshed Model with Kerr Law Nonlinearity, International Journal of Modern Physics B, 35 (2021), 26, ID 2150263
  7. He, J. H., et al., Two Exact Solutions to the General Relativistic Binet's Equation, Astrophysics And Space Science, 323 (2009),1, pp. 97-98
  8. Akram, G., et al., The Dynamical Study of Biswas-Arshed Equation via Modified Auxiliary Equation Method, Optik, 255 (2022), ID 168614
  9. Ain, Q. T., et al., An Analysis of Time-Fractional Heat Transfer Problem Using Two-Scale Approach, GEM-International Journal on Geomathematics, 12 (2021), 1, pp. 1-10
  10. Qian, M. Y., et al., Two-Scale Thermal Science for Modern life-Making the Impossible Possible, Thermal Science, 26 (2022), 3B, pp. 2409-2412
  11. Kumar, S., et al., A Study of Fractional Lotka-Volterra Population Model Using Haar Wavelet and Adams-Bashforth-Moulton Methods, Mathematical Methods In the Applied Sciences, 43 (2020), 8, pp. 5564-5578
  12. Nadeem, M., et al., He-Laplace Variational Iteration Method for solving the Nonlinear Equations Arising in Chemical Kinetics and Population Dynamics, Journal of Mathematical Chemistry, 59 (2021), 2, pp. 1234-1245
  13. Wang, K. J., et al., Diverse Optical Solitons to the Radhakrishnan-Kundu-Lakshmanan Equation for the Light Pulses, Journal of Nonlinear Optical Physics & Materials, On-line first,, 2023
  14. Yang, X.J., et al., Exact Travelling Wave Solutions for the Local Fractional Two-Dimensional Burgers-type Equations, Computers and Mathematics with Applications, 73 (2017), 2, pp. 203-210
  15. Liu, J.-G., et al., On the (N+1)-Dimensional Local Fractional Reduced Differential Transform Method and Its Applications, Mathematical Methods in the Applied Sciences, 43 (2020), 15, pp. 8856-8866
  16. Wang, K. J., Resonant Multiple Wave, Periodic Wave and Interaction Solutions of the New Extended (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation, Nonlinear Dynamics, On-line firsst,, 2023
  17. Yang, X. J., et al., On the Traveling-Wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos, 26 (2016), ID 084312
  18. Xu, C. J., et al., Modeling and Analysis Fractal Order Cancer Model with Effects of Chemotherapy, Chaos Solitons and Fractals, 161 (2022), 112325
  19. Nisar, K. S., et al., An Analysis of Controllability Results for Nonlinear Hilfer Neutral Fractional Derivatives with Non-Dense Domain, Chaos, Soliton and Fractals, 146 (2021), 2, ID 110915
  20. Ozkan, Y. S., et al., Novel Multiple Soliton and Front Wave Solutions for the 3D-Vakhnenko-Parkes Equation, Modern Physics Letters B, 36 (2022), 9, ID 2250003
  21. Baskonus, N. M., et al., Complex Mixed Dark-Bright Wave Patterns to the Modified Vakhnenko-Parkes Equations, Alexandria Engineering Journal, 59 (2020), 2, pp. 2149-2160
  22. Wazwaz, A. M., The Integrable Vakhnenko-Parkes (VP) and the Modified Vakhnenko-Parkes (MVP) Equations: Multiple Real and Complex Soliton Solutions, Chinese Journal of Physics, 57 (2019) , 2, pp. 375-381
  23. Wang, K. L., A New Fractal Model for the Soliton Motion in a Microgravity Space, International Journal of Numerical Methods for Heat & Fluid flow, 31 (2021), 1, pp. 442-451
  24. Yang, X. J., et al., Cantor-Type Cylindrical Method for Differential Equations with Local Fractional Derivative, Physics Letters A, 377 (2015), 28, pp. 1696-1700
  25. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press. New York, USA, 2015

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence