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<p>In this paper, we apply Picard’s method to solve fractal differential equations arising in both ordinary and partial forms. We begin with a brief review of fractal calculus and introduce the Fractal Picard Iteration Method. This method is then used to solve ordinary and partial fractal differential equations systematically. As applications, we demonstrate the effectiveness of the approach by solving the fractal model of an RL circuit and the Schrödinger equation for a free particle. The results highlight the adaptability and strength of Picard’s method in addressing problems within fractal frameworks.</p>

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Picard’s Method for Solving Fractal Differential Equations

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Alireza Khalili Golmankhaneh

摘要

In this paper, we apply Picard’s method to solve fractal differential equations arising in both ordinary and partial forms. We begin with a brief review of fractal calculus and introduce the Fractal Picard Iteration Method. This method is then used to solve ordinary and partial fractal differential equations systematically. As applications, we demonstrate the effectiveness of the approach by solving the fractal model of an RL circuit and the Schrödinger equation for a free particle. The results highlight the adaptability and strength of Picard’s method in addressing problems within fractal frameworks.