In this paper, we solve the fractal nonlinear Klein-Gordon equation using the Homotopy Perturbation Method (HPM). The method effectively demonstrates how the solution evolves over time in relation to the fractal dimensions of space and time. To illustrate the approach, several examples are presented, showcasing the details of the solution process. These examples highlight the applicability of HPM for addressing complex fractal differential equations and provide insights into the behavior of solutions within fractal geometries.

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Fractal Nonlinear Klein-Gordon Equation

  • Alireza Khalili Golmankhaneh,
  • Lucero Damián

摘要

In this paper, we solve the fractal nonlinear Klein-Gordon equation using the Homotopy Perturbation Method (HPM). The method effectively demonstrates how the solution evolves over time in relation to the fractal dimensions of space and time. To illustrate the approach, several examples are presented, showcasing the details of the solution process. These examples highlight the applicability of HPM for addressing complex fractal differential equations and provide insights into the behavior of solutions within fractal geometries.