微分与积分算子的分数幂及其在加速器物理与技术中的应用
经典分析与常微分方程
2020-04-07 v1 数学物理
math.MP
加速器物理
摘要
在本文中，我们提出了一种新方法来求解阶数为 3/2 的分数阶积分。该积分出现在求解 Biot-Savart 方程以寻找螺线管磁场分量的精确解析解的过程中。我们通过割断支线（branch line）来求解该积分，以便在积分内部获得解析函数而非多值运算。
引用
@article{arxiv.2004.01700,
title = {Fractional Powers of the Differentiation and Integration Operators and its Application in Accelerator Physics and Technology},
author = {Mostafa Behtouei and Luigi Faillace and Luigi Palumbo and Bruno Spataro and Alessandro Variola and Mauro Migliorati},
journal= {arXiv preprint arXiv:2004.01700},
year = {2020}
}
备注
Portions of this manuscript has been published in our previous paper with arXiv:2002.09444. In this paper we describe and analyze the mathematical process used in our previous paper with arXiv:2002.09444