分形变分：一个新的框架

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-09-20 DOI:10.1007/s13324-025-01128-9

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

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引用次数: 0

摘要

本文对分形演算作了简要的概述。引入微积分中分形变分的概念，推导了分形欧拉方程的一般形式，并给出了另一种形式。我们探索了分形欧拉方程的应用，包括黑洞视界附近的光学分形路径和分形空间中最短距离的确定。文中提供了实例和图解来说明这些方程的详细行为及其实际意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fractal Calculus of Variations: A New Framework

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.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.