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A Modern Traveling Wave Solution For Caputo-Fractional Klein–Gordon Equations

Author

Listed:
  • AHMAD EL-AJOU

    (Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan)

  • RANIA SAADEH

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

  • ALIAA BURQAN

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

  • MAHMOUD ABDEL-ATY

    (Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt4Deanship of Graduate Studies and Research, Ahlia University, Manama 10878, Bahrain)

Abstract

This research paper introduces a novel approach to deriving traveling wave solutions (TWSs) for the Caputo-fractional Klein–Gordon equations. This research presents a distinct methodological advancement by introducing TWSs of a particular time-fractional partial differential equation, utilizing a non-local fractional operator, specifically the Caputo derivative. To achieve our goal, a novel transformation is considered, that converts a time-fractional partial differential equation into fractional ordinary differential equations, enabling analytical solutions through various analytical methods. This paper employs the homotopy analysis method to achieve the target objectives. To demonstrate the efficiency and applicability of the proposed transform and method, two examples are discussed and analyzed in figures.

Suggested Citation

  • Ahmad El-Ajou & Rania Saadeh & Aliaa Burqan & Mahmoud Abdel-Aty, 2024. "A Modern Traveling Wave Solution For Caputo-Fractional Klein–Gordon Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:05:n:s0218348x24500841
    DOI: 10.1142/S0218348X24500841
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