Matrices have important applications of statistical analysis, circuits, mechanics, optics, and quantum physics. In this article, matrix explicit formulas of the exponentials for computing exp(αA), where A is a special n × n matrix and α is the order of fractional derivative, were obtained. The definitions of the fractional derivative respectively are the Caputo fractional derivative and Riemann-Liouville fractional derivative. Here, we need to point that the new results can be looked as an extended the previous work of the authors. The explicit formulas can help us better to explore deep connotations from natural science.

中文翻译：

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一些带有分数阶导数的特殊矩阵的新显式公式：II

矩阵在统计分析、电路、力学、光学和量子物理学方面有着重要的应用。在本文中，得到了计算exp(αA)的指数的矩阵显式公式，其中A是一个特殊的n×n矩阵，α是分数阶导数。分数阶导数的定义分别是 Caputo 分数阶导数和 Riemann-Liouville 分数阶导数。在这里，我们需要指出，新的结果可以看作是作者之前工作的扩展。显式的公式可以帮助我们更好地探索自然科学的深层内涵。