论文标题
带有Hilfer分数衍生物的电介质中的异常松弛
Anomalous relaxation in dielectrics with Hilfer fractional derivative
论文作者
论文摘要
我们以与Debye，Cole-Cole，Davidson-Cole和Havriliak-Negami经验引入的宽松函数相同的方式，根据任意参数作为动力学方程的解决方案引入新的放松函数，这是介质中的异常弛豫，这些放松被恢复为特定情况。我们提出了一个微分方程，该方程式引入了一个用0 <ξ<1和typeη的Hilfer分数衍生物编写的分数算子，并以0 <η<1。为了讨论分数微分方程的解，需要拉普拉斯变换的方法。作为产品，我们提到了解决方案完全单调的特殊情况。最后，将经验模型恢复为特定情况。
We introduce a new relaxation function depending on an arbitrary parameter as solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami, anomalous relaxation in dielectrics, which are recovered as particular cases. We propose a differential equation introducing a fractional operator written in terms of the Hilfer fractional derivative of order ξ, with 0<ξ<1 and type η, with 0<η<1. To discuss the solution of the fractional differential equation, the methodology of Laplace transform is required. As a by product we mention particular cases where the solution is completely monotone. Finally, the empirical models are recovered as particular cases.
