从分形算法出发的简单分形演算
Simple fractal calculus from fractal arithmetic
摘要：
从布尔金型的基本非丢番图算术运算开始的非牛顿微积分适用于基数是连续的所有分形。由此产生的导数和积分的定义比在更传统的文献中找到的要简单，并且它们通常在标准方法失败的情况下工作。作为一个例子，我们执行一个实值函数的Sierpienski集域的傅里叶变换。由此产生的形式主义是一样简单的通常的本科微积分。
英文摘要：
Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued function with Sierpiński-set domain. The resulting formalism is as simple as the usual undergraduate calculus.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
