The various aspects of differential calculus are always on the path to progress and excellence, and these trends have been more highlighted in recent decades. More specifically, tremendous advances have been made in the field of fractional calculus. One of the main branches in this field is the local fractional derivative, which has been used successfully to describe many real-world phenomena in science, and engineering. The present contribution aims to adopt a newly proposed analytical technique to construct exact solutions to local fractional Schamel's equation defined on Cantor sets. To this end, a set of elementary functions are constructed on Cantor sets is defined. Furthermore, the combination of these modified functions is utilized to constitute a formal representation of the searched exact solution for the equation. Numerical simulations related to some of the obtained solutions are also included. The acquired results confirm that the method used is not only very straightforward but also efficient in terms of application. In order to perform complicated and tedious calculations while solving this problem, the use of a symbolic computational packages in Maple or Mathematica is inevitable. The work emphasizes the power of the employed method in providing various exact solutions to different physical problems involving local fractional derivatives.

中文翻译：

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关于在康托集上具有局部分数导数的 Schamel 方程的不可微精确解

微积分的各个方面总是在进步和卓越的道路上，而这些趋势在近几十年来更加突出。更具体地说，在分数阶微积分领域已经取得了巨大的进步。该领域的主要分支之一是局部分数导数，它已成功地用于描述科学和工程中的许多现实世界现象。目前的贡献旨在采用一种新提出的分析技术来构建定义在康托集上的局部分数沙梅尔方程的精确解。为此，定义了一组在康托集上构造的初等函数。此外，这些修改后的函数的组合用于构成搜索到的方程精确解的形式表示。还包括与一些获得的解决方案相关的数值模拟。获得的结果证实，所使用的方法不仅非常简单，而且在应用方面也很有效。为了在解决这个问题的同时执行复杂繁琐的计算，在 Maple 或 Mathematica 中使用符号计算包是不可避免的。这项工作强调了所采用的方法在为涉及局部分数导数的不同物理问题提供各种精确解决方案方面的力量。在 Maple 或 Mathematica 中使用符号计算包是不可避免的。这项工作强调了所采用的方法在为涉及局部分数导数的不同物理问题提供各种精确解决方案方面的力量。在 Maple 或 Mathematica 中使用符号计算包是不可避免的。这项工作强调了所采用的方法在为涉及局部分数导数的不同物理问题提供各种精确解决方案方面的力量。