THERMAL SCIENCE

International Scientific Journal

THE LAPLACE SERIES SOLUTION FOR LOCAL FRACTIONAL KORTEWEG-DE VRIES EQUATION

ABSTRACT
In this paper, we consider a new application of the local fractional Laplace series expansion method to handle the local fractional Korteweg-de Vries equation. The obtained solution with non-differentiable type shows that the technology is accurate and efficient.
KEYWORDS
PAPER SUBMITTED: 2016-02-01
PAPER REVISED: 1970-01-01
PAPER ACCEPTED: 1970-01-01
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3867Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S867 - S870]
REFERENCES
  1. Yang, X.-J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
  2. Yang, X.-J., et al., An Asymptotic Perturbation Solution for a Linear Oscillator of Free Damped Vibrations in Fractal Medium Described by Local Fractional Derivatives, Communications in Nonlinear Science and Numerical Simulation, 29 (2015), 1, pp. 499-504
  3. Liu, H. Y., et al., Fractional Calculus for Nanoscale Flow and Heat Transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014), 6, pp. 1227-1250
  4. Yang, X.-J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 145 (2016), 1, pp. 1-12
  5. Cao, Y., Ma, W. G., et al., Local Fractional Functional Method for Solving Diffusion Equations on Cantor Sets, Abstract Applied Analysis, 2014 (2014), ID 803693
  6. 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.
  7. Yang, X.-J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47 (2015), Sept., pp. 54-60
  8. Yang, X.-J., et al., A New Numerical Technique for Solving the Local Fractional Diffusion Equation: Two-Dimensional Extended Differential Transform Approach, Applied Mathematics and Computation, 274 (2016), Feb., pp. 143-151
  9. 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
  10. Jassim, H. K., et al., Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015 (2015), ID 309870
  11. Baleanu, D., et al., On the Exact Solution of Wave Equations on Cantor Sets, Entropy, 17 (2015), 9, pp. 6229-6237
  12. Goswami, P., et al., On the Solution of Local Fractional Differential Equations Using Local Fractional Laplace Variational Iteration Method, Mathematical Problems in Engineering, 2016 (2016), ID 9672314
  13. Ahmad, J., et al., Analytic Solutions of the Helmholtz and Laplace Equations by Using Local Fractional Derivative Operators, Waves, Wavelets and Fractals, 1 (2015), 1, pp. 22-26
  14. Yang, X.-J., et al., Initial-Boundary Value Problems for Local Fractional Laplace Equation Arising in Fractal Electrostatics, Journal of Applied Nonlinear Dynamics, 4 (2015), 3, pp. 349-356
  15. Yan, S. P., Local Fractional Laplace Series Expansion Method for Diffusion Equation Arising in Fractal Heat Transfer, Thermal Science, 17 (2015), Suppl. 1, pp. S131-S135

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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