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Exact Travelling Wave Solutions for Local Fractional Partial Differential Equations in Mathematical Physics

  • Xiao-Jun YangEmail author
  • Feng Gao
  • J. A. Tenreiro Machado
  • Dumitru Baleanu
Chapter
First Online:
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 24)

Abstract

In the article, we investigate the exact travelling wave solutions for the linear and nonlinear local fractional partial differential equations. The non-differential exact solutions of the fractal diffusion, Korteweg-de Vries, and Boussinesq equations via local fractional derivative are discussed in detail. The local fractional calculus formulations are efficient in description of fractal and complex behaviors of the linear and nonlinear mathematical physics.

Keywords

Exact Traveling Wave Solutions Local Fractional Derivative (LFD) Boussinesq Equations Fractional Diffusion Nonlinear Mathematical Physics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

This work is supported by the State Key Research Development Program of the People’s Republic of China (Grant No.2016YFC0600705), the Natural Science Foundation of China (Grant No.51323004), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD2014).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Xiao-Jun Yang
    • 1
    • 2
    Email author
  • Feng Gao
    • 1
    • 2
  • J. A. Tenreiro Machado
    • 3
  • Dumitru Baleanu
    • 4
  1. 1.State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.School of Mechanics and Civil EngineeringChina University of Mining and TechnologyXuzhouChina
  3. 3.Instituto Superior de Engenharia do PortoPortoPortugal
  4. 4.Department of MathematicsÇankaya UniversityAnkaraTurkey

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