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

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Mathematical Methods in Engineering

Part of the book series: Nonlinear Systems and Complexity ((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.

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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).

Author information

Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, China

    Xiao-Jun Yang & Feng Gao

  2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, China

    Xiao-Jun Yang & Feng Gao

  3. Instituto Superior de Engenharia do Porto, Porto, Portugal

    J. A. Tenreiro Machado

  4. Department of Mathematics, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

Authors
  1. Xiao-Jun Yang
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  2. Feng Gao
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  3. J. A. Tenreiro Machado
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  4. Dumitru Baleanu
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Corresponding author

Correspondence to Xiao-Jun Yang .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Cankaya University, Ankara, Turkey

    Kenan Taş

  2. Department of Mathematics, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Instituto Superior de Engenharia do Porto, Porto, Portugal

    J. A. Tenreiro Machado

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Yang, XJ., Gao, F., Tenreiro Machado, J.A., Baleanu, D. (2019). Exact Travelling Wave Solutions for Local Fractional Partial Differential Equations in Mathematical Physics. In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-90972-1_12

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  • DOI: https://doi.org/10.1007/978-3-319-90972-1_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90971-4

  • Online ISBN: 978-3-319-90972-1

  • eBook Packages: EngineeringEngineering (R0)

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