THERMAL SCIENCE

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Shu-Xian Deng

,

Xin-Xin Ge

ANALYTICAL SOLUTION TO LOCAL FRACTIONAL LANDAU-GINZBURG-HIGGS EQUATION ON FRACTAL MEDIA

ABSTRACT
The main objective of the present article is to introduce a new analytical solution of the local fractional Landau-Ginzburg-Higgs equation on fractal media by means of the local fractional variational iteration transform method, which is coupling of the variational iteration method and Yang-Laplace transform method.
KEYWORDS
Landau-Ginzburg-Higgs equation, fractal media, Yang-Laplace transform, variational iteration method
PAPER SUBMITTED: 2020-03-03
PAPER REVISED: 2020-03-20
PAPER ACCEPTED: 2020-06-20
PUBLISHED ONLINE: 2021-12-24
DOI REFERENCE: https://doi.org/10.2298/TSCI2106449D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 6, PAGES [4449 - 4455]
REFERENCES
  1. Palvelev, R. V., et al., Justification of the Adiabatic Principle for Hyperbolic Ginzburg-Landau Equations, Proceedings of the Steklov Institute of Mathematics, 1 (2012), 277, pp. 191-205
  2. Iftikhar, A., et al., Solutions of (2+1) Dimensional Generalized KdV, Sin Gordon and Landau-Ginzburg-Higgs Equations, Scientific Research and Essays, 28 (2013), 8, pp. 1349-1359
  3. Arnous, A. H., et al., Backlund Transformation of Fractional Riccati Equation and Its Applications to the Space-Time FDEs, Mathematical Methods in the Applied Sciences, 38 (2015), 18, pp. 4673-4678
  4. Mo, J. Q., et al., Perturbation Theory of Soliton Solutions for a Generalized Landau-Ginzburg-Higgs Equation, Acta Physica Sinica, 12 (2005), 54, pp. 5581-5584
  5. Shang, Y. D., Explicit and Exact Solutions for a Class of Nonlinear Wave Equation, Acta Mathematicae Applicatae Sinica, 1 (2000), 23, pp. 21-30
  6. Doha, E. H., et al., A Shifted Jacobi Collocation Algorithm for Wave Type Equations with Non-Local Conservation Conditions, Central European Journal of Physics, 9 (2014), 12, pp. 637-653
  7. Khater, M., et al., Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation, Mathematical and Computational Applications, 1 (2019), 24, pp. 1-10
  8. Yang, X. J., et al., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 2 (2013), 17, pp. 625-628
  9. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
  10. Yang, X. J., Heat Transfer in Discontinuous Media, Advances in Mechanical Engineering and Its Applications, 3 (2012), 1, pp. 47-53
  11. Yang, X. J., Local Fractional Partial Differential Equations with Fractal Boundary Problems, Advances in Computational Mathematics and Its Applications, 1 (2012), 1, pp. 60-63
  12. Yang, X. J., Baleanu, D., Local Fractional Variational Iteration Method for Fokker-Planck Equation on a Cantor Set, Acta Universitaria, 2 (2013), 23, pp. 3-8
  13. Baleanu, D., et al., Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets, Abstract and Applied Analysis, 2014 (2014), ID 535048
  14. Yan, S. P., et al., Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014 (2014), ID 161580
  15. Jafari, H., Jassim, H. K., Local Fractional Series Expansion Method for Solving Laplace and Schrodinger Equations on Cantor Sets within Local Fractional Operators, International Journal of Mathematics and Computer Research, 11 (2014), 2, pp. 736-744
  16. Jacobs, B. A., High-Order Compact Finite Difference and Laplace Transform Method for the Solution of Time-Fractional Heat Equations with Dirchlet and Neumann Boundary Conditions, Numerical Methods for Partial Differential Equations, 4 (2016), 3, pp. 1184-1199
  17. He, J. H., Some Applications of Nonlinear Fractional Differential Equations and Their Approximations, Bulletin of Science, Technology and Society, 2 (1999), 15, pp. 86-90
  18. Mainardi, F., et al., The Fundamental Solution of the Space-Time Fractional Diffusion Equation, Fractional Calculus and Applied Analysis, 2 (2001), 4, pp. 153-192
  19. Rida S. Z., et al., On the Solutions of Time-Fractional Reaction-Diffusion Equations, Communications in Nonlinear Science and Numerical Simulation, 12 (2010), 15, pp. 3847-3854
  20. Debnath, L., Fractional Integral and Fractional Differential Equations in Fluid Mechanics, Fractional Calculus and Applied Analysis, 2 (2003), 6, pp. 119-155
  21. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
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Analytical solution to local fractional Landau-Ginzburg-Higgs equation on fractal media

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