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<p>In this paper, we give a short summary of fractal calculus. We introduce the concept of fractal variation of calculus and derive the general form of the fractal Euler equation, along with an alternate form. We explore applications of the fractal Euler equation, including the optical fractal path near the event horizon of a black hole and determining the shortest distance in fractal space. Examples and illustrative plots are provided to demonstrate the detailed behavior of these equations and their practical implications.</p>

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Fractal Calculus of Variations: A New Framework

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Alireza Khalili Golmankhaneh,
  • Cemil Tunç,
  • Claude Depollier,
  • Ahmed I. Zayed

摘要

In this paper, we give a short summary of fractal calculus. We introduce the concept of fractal variation of calculus and derive the general form of the fractal Euler equation, along with an alternate form. We explore applications of the fractal Euler equation, including the optical fractal path near the event horizon of a black hole and determining the shortest distance in fractal space. Examples and illustrative plots are provided to demonstrate the detailed behavior of these equations and their practical implications.