In this paper, we made improvement on the conformable fractional derivative. Compared to the original one, the improved conformable fractional derivative can be a better replacement of the classical Riemann-Liouville and Caputo fractional derivative in terms of physical meaning. We also gave the definition of the corresponding fractional integral and illustrated the applications of the improved conformable derivative to fractional differential equations by some examples.

中文翻译：

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相容分数阶导数的改进及其在分数阶微分方程中的应用

在本文中，我们对适形分数导数进行了改进。与原始的分数导数相比，改进后的分数分数导数在物理意义上可以更好地替代经典的黎曼-利维尔和卡普托分数导数。我们还给出了相应的分数积分的定义，并通过一些示例说明了改进的适形导数在分数微分方程中的应用。