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Traveling-wave solutions of the Klein–Gordon equations with M-fractional derivative

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Abstract

Based on two algorithm integrations, such as the \(\exp (-\Phi (\xi ))\)-expansion method and the hyperbolic function method, we build dark, bright and trigonometric function solution to the Klein–Gordon equations with M-fractional derivative of order \(\alpha \). By adopting the travelling-wave transformation, the constraint condition between the model coefficients and the travelling-wave frequency coefficient for the existence of soliton solutions is also obtained. Moreover, miscellaneous soliton solutions obtained is depicted in 3D and 2D.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon

    Alphonse Houwe

  2. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

  3. Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030 , Eskisehir, Turkey

    Ahmet Bekir

  4. Department of Physics, Faculty of Science, The University of Ngaoundere, Ngaoundere, Cameroon

    Serge Y Doka

Authors
  1. Alphonse Houwe
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  2. Hadi Rezazadeh
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  3. Ahmet Bekir
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  4. Serge Y Doka
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Houwe, A., Rezazadeh, H., Bekir, A. et al. Traveling-wave solutions of the Klein–Gordon equations with M-fractional derivative. Pramana - J Phys 96, 26 (2022). https://doi.org/10.1007/s12043-021-02254-2

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  • DOI: https://doi.org/10.1007/s12043-021-02254-2

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