论文标题
通过$ n $ th级衍生物的分数松弛方程的完全单调性。
On complete monotonicity of solution to the fractional relaxation equation with the $n$th level fractional derivative
论文作者
论文摘要
在本文中，我们首先针对$ n $ the级分数衍生物及其拉普拉斯变换的投影仪的明确公式。然后讨论了带有$ n $ th级分数衍生物的分数松弛方程。事实证明，在某些条件下，该方程式的初始值问题的解决方案是完全单调函数，可以用Mittag-Leffler功能的线性组合形式表示，并具有某些功率定律权重。特别注意与第二级衍生物的松弛方程式。
In this paper, we first deduce the explicit formulas for the projector of the $n$th level fractional derivative and for its Laplace transform. Then the fractional relaxation equation with the $n$th level fractional derivative is discussed. It turns out that under some conditions, the solutions to the initial-value problems for this equation are completely monotone functions that can be represented in form of the linear combinations of the Mittag-Leffler functions with some power law weights. Special attention is given to the case of the relaxation equation with the 2nd level derivative.
