标题： 分数阶微分熵及其在建模一维流速中的应用 显示英文标题

标题： Fractional differential entropy and its application in modeling one-dimensional flow velocity

摘要： 分数阶Shannon熵的推广由Ubriaco提出，已针对离散分布进行了研究。 在本文中，我们对这种熵的连续模拟进行了详细研究，称为分数阶微分熵，并发现了一些有趣的特性，使其在文献中现有的熵中脱颖而出。 所研究的熵度量对于一些著名的连续分布进行了分析和数值评估，这在可靠性分析工作和其他复杂系统的统计研究中将非常有用。 此外，它已被用于模拟宽渠道中湍流流动的一维垂直速度分布。 使用了一种单参数的空间分布函数，以更好地估计速度分布。 通过回归分析，利用实验和现场数据验证了该模型的有效性。 还进行了比较研究，以展示所提出的模型相对于现有基于熵的模型的优势。 显示英文摘要

摘要： The fractional order generalization of Shannon entropy proposed by Ubriaco has been studied for discrete distributions. In the current paper, we conduct a detailed study of the continuous analogue of this entropy termed as fractional differential entropy and find some interesting properties which makes it stand out among the existing entropies in literature. The studied entropy measure is evaluated analytically and numerically for some well-known continuous distributions, which will be quite useful in reliability analysis works and other statistical studies of complex systems. Further, it has been used to model the one-dimensional vertical velocity profile of turbulent flows in wide open channels. A one-parametric spatial distribution function is utilized for better estimation of the velocity distribution. The validity of the model has been established using experimental and field data through regression analysis. A comparative study is also presented to show the superiority of the proposed model over the existing entropy-based models.