THERMAL SCIENCE

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Yong-Ju Yang

,

Shun-Qin Wang

A LOCAL FRACTIONAL HOMOTOPY PERTURBATION METHOD FOR SOLVING THE LOCAL FRACTIONAL KORTEWEG-DE VRIES EQUATIONS WITH NON-HOMOGENEOUS TERM

ABSTRACT
In this paper, a local fractional homotopy perturbation method is presented to solve the boundary and initial value problems of the local fractional Korteweg-de Vries equations with non-homogeneous term. In order to demonstrate the validity and reliability of the method, two types of the Korteweg-de Vries equations with non-homogeneous term are proposed.
KEYWORDS
local fractional homotopy perturbation method, local fractional derivative, local fractional Korteweg-de Vries equation
PAPER SUBMITTED: 2018-08-22
PAPER REVISED: 2018-11-20
PAPER ACCEPTED: 2019-01-05
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180822216Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 3, PAGES [1495 - 1501]
REFERENCES
  1. Eltantawy, S. A., et al., Nonlinear Structures of the Korteweg-de Vries and Modified Korteweg-de Vries Equations in Non-Maxwellian Electron-positron-ion Plasma: Solitons Collision and Rogue Waves, Physics of Plasmas, 21 (2014), 5, pp.46-75
  2. Yang, X. J., et al., Modelling Fractal Waves on Shallow Water Surfaces Via Local Fractional Korteweg-de Vries Equation, Abstract and Applied Analysis, 2014,(2014), pp.1-9
  3. Zhao, X H., et al., Solitons, Periodic Waves, Breathers and Integrability for a Nonisospectral and Variable-Coefficient Fifth-Order Korteweg-De Vries Equation in Fluids, Applied Mathematics Letters, 65 (2017), 2, pp.48-55
  4. De, B A., et al., White Noise Driven Korteweg-de Vries Equation ,Journal of Functional Analysis, 169 (1999), 2, pp.532-558
  5. Yan, J L., et al., A New High-order Energy-preserving Scheme for the Modified Korteweg-de Vries Equation, Numerical Algorithms,74 (2016), 3, pp.1-16
  6. Khusnutdinova, K R., et al., Soliton Solutions to the Fifth-order Korteweg - de Vries Equation and Their Applications to Surface and Internal Water Waves. Physics of Fluids, 30 (2018), 2, pp. 928-941
  7. Liu, F, et al., TDGL and mKdV Equations for Car-following Model Considering Traffic Jerk, Nonlinear Dynamics,83 (2015), 1-2, pp. 1-8
  8. Tauseef Mohyud-Din, et al., Homotopy Analysis Method for Space-and time-fractional KdV Equation, Int. J. Numer. Methods Heat Fluid Flow ,22 (2012), 7, pp. 928-941
  9. Momani., S, et al., Variational Iteration Method for Solving the Space-and time-fractional KdV Equation, Numer. Methods Partial Differ. Equations, 24 (2008), 1, pp.262-271
  10. Matinfar, M., et al., The Functional Variable Method for Solving the Fractional Korteweg-de Vries Equations and the Coupled Korteweg-de Vries Equations, Pramana, 85 (2015), 4, pp.583-592
  11. Yang, X J., Local Fractional Functional Analysis and Its Applications, Asian Academic publisher Limited, Hong Kong, China, 2011
  12. Yang, X J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  13. Yang, X J., et al., On Exact Traveling-wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos, 26 (2016), 8, pp.110-118
  14. Singh J, et al., A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow, Entropy,18 (2016), 6, pp. 206-213
  15. Yang, X J., et al., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science,17 (2013), 2, pp. 625-628
  16. Yang, Y. J., et al., A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abstract and Applied Analysis,2013(2013), pp.1-6.
  17. Liu, C. F., et al., Reconstructive Schemes for Variational Iteration Method Within Yang-Laplace Transform with Application to Fractal Heat Conduction Problem, Thermal Science, 17 (2013), 3, pp. 715-721
  18. Yang, Y J., et al., Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method, Advances in Mathematical Physics, 2013(2013), pp.1-6
  19. Yang, X J., et al., Variational Iteration Transform Method for Fractional Differential Equations with Local Fractional Derivative, Abstract and Applied Analysis,2014(2014), pp.1-9
  20. Yang, X. J., et al., New Analytical Solutions for Klein-Gordon and Helmholtz Equations in Fractal Dimensional Space, Proceedings of the Romanian Academy - Series A: Mathematics, Physics, Technical Sciences, Information Science, 18(2017), 3, pp.231-238
  21. Yang, X. J., et al., New Rheological Models within Local Fractional Derivative, Romanian Reports in Physics, 69(2017), 3, pp.1-8
  22. Yang, X. J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 151(2017), 1-4, pp.63-75
  23. Hemeda, A. A., et al., Local Fractional Analytical Methods for Solving Wave Equations with Local Fractional Derivative, Mathematical Methods in the Applied Sciences, 41(2018), 6, pp.2515-2529
  24. Yang, X. J., et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67(2015), 3, pp.752-761
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A local fractional homotopy perturbation method for solving the local fractional Korteweg-de Vries equations with non-homogeneous term

© 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