一个概括的对称潜能核的相差混合积分方程及其在 (3+1) 维度中的物理含义
1Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah, Saudi Arabia.
Heliyon
|February 21, 2025
概括
这项研究分析了时间对核结构的影响,使用一种新的相滞后混合积分方程 (P-LMIE) 方法. 它引入了一种新的方法来理解3D积分方程中的时间变化.
科学领域:
- 数学物理 数学物理
- 积分方程 积分方程 积分方程
- 分数微积分的计算.
背景情况:
- 没有先前的研究研究了时间对核结构的影响或3D积分方程中的时间延迟.
- 积分方程的时间变化仍然是一个未被充分探索的领域.
研究的目的:
- 分析一个 (3+1) 维相差混合积分方程 (P-LMIE).
- 调查时间变化和时间延迟对积分方程的影响.
- 开发一个框架来理解数学物理中的时间依赖现象.
主要方法:
- 将胡克定律应用于位置内核作为通用潜力.
- 利用分数运算的属性来导出一个整微分的弗雷德霍姆-沃尔特拉积分方程 (Io-DF-VIE).
- 使用分离方法将P-LMIE转换为m-harmonic Fredholm积分方程 (FIEs).
- 使用退化方法推断一个线性代数系统 (LAS).
- 杆式Maple 2018和数值计算的数学编程.
主要成果:
- 从分析的积分方程中导出新的实例.
- 成功地将P-LMIE转换为具有特定内核形式的m-harmonicFIE.
- 获得一个线性代数系统 (LAS) 进行分析.
- 韦伯-索尼恩积分系数和度的计算数值.
结论:
- 该研究为时间依赖的积分方程提供了一个新的分析框架.
- 开发的方法为原子核和积分方程的时间结构提供了新的见解.
- 这些发现有助于分数微积分和数学物理学领域.
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