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摘要翻译：
有许多函数处处连续，但在某些点或全部点不可微，这类函数称为不可达函数。表示这类不可达函数的图称为不可达图。例如，心电就是这样一个不可达的图形。经典微积分在它们的表征上失败了，因为导数在不可达的点上不存在。这种不可达函数可以用分数阶微积分来表征，因为在不存在经典导数的不可达点上存在分数阶导数。分数阶导数的定义是由Grunwald-Letinikov、Riemann-Liouville、Caputo和Jumarie等数学家提出的，以发展分数阶微积分的理论。本文利用Jumarie型分数阶导数，得到了相变（P.T.）它是左分数阶导数和右分数阶导数的区别，用来表征这些点。利用上述数学工具，对正常心电图和问题心电图（右室肥厚）进行了对比研究。
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英文标题：
《Application of Fractional Derivatives in Characterization of ECG graphs
of Right Ventricular Hypertrophy Patients》
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作者：
Srijan Sengupta, Uttam Ghosh, Susmita Sarkar and Shantanu Das
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最新提交年份：
2017
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分类信息：
一级分类：Quantitative Biology 数量生物学
二级分类：Other Quantitative Biology 其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
There are many functions which are continuous everywhere but non-differentiable at some or all points such functions are termed as unreachable functions. Graphs representing such unreachable functions are called unreachable graphs. For example, ECG is such an unreachable graph. Classical calculus fails in their characterization as derivatives do not exist at the unreachable points. Such unreachable functions can be characterized by fractional calculus as fractional derivatives exist at those unreachable points where classical derivatives do not exist. Definition of fractional derivatives has been proposed by several mathematicians like Grunwald-Letinikov, Riemann-Liouville, Caputo, and Jumarie to develop the theory of fractional calculus. In this paper, we have used Jumarie type fractional derivative and consequently the phase transition (P.T.) which is the difference between left fractional derivative and right fractional derivatives to characterize those points. A comparative study has been done between normal ECG sample and problematic ECG sample (Right Ventricular Hypertrophy) by the help of the above mentioned mathematical tool.
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PDF链接：
https://arxiv.org/pdf/1711.02332
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