A MODERN TRAVELING WAVE SOLUTION FOR CAPUTO-FRACTIONAL KLEIN–GORDON EQUATIONS

Ahmad El-Ajou (), Rania Saadeh, Aliaa Burqan () and Mahmoud Abdel-Aty
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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

FRACTALS (fractals), 2024, vol. 32, issue 05, 1-13

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.

Keywords: Non-Local Fractional Derivative; Traveling Wave Solution; Klein–Gordon Equation; Approximate Method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500841

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