关于分析和更深层次的属性,分数复杂的物理模型,涉及到非单一的核心
Emad Fadhal1, Abdul Hamid Ganie2, N S Alharthi3
1Department of Mathematics & Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa, 31982, Saudi Arabia. efadhal@kfu.edu.sa.
Scientific reports
|September 27, 2024
概括
本研究应用了自然变换分解法来解决量子场理论中的分数微分方程. 该方法为复杂的模型提供了准确的近似,例如巨大的Thirring模型,通过图形分析验证.
科学领域:
- * 数学物理数学物理
- * * 量子场理论 量子场理论
- * 非线性动力学
背景情况:
- * 大规模的蒂林模型涉及合的非线性复杂微分方程,在量子场理论中至关重要.
- * 分数微积分为模拟复杂物理现象提供了一个更普遍的框架.
- * 现有的方法在解决这些复杂的分数微分方程时可能缺乏效率.
研究的目的:
- * 解决结合的分数微分方程,管理大规模的蒂林模型和昆杜·埃克豪斯方程.
- * 为了研究自然变换分解法 (NTDM) 与不同的分数导数的适用性.
- * 为这些非线性模型开发准确和高效的近似分析解决方案.
主要方法:
- *自然转化分解方法 (NTDM) 的应用.
- *使用分数导数,特别是卡普托-法布里齐奥和阿坦加纳-巴莱努类型.
- *将NTDM与阿多米亚分解方案相结合,以提高准确性.
主要成果:
- * NTDM成功地为研究的分数微分方程生成了快速合的序列解决方案.
- * 数字结果证明了拟议方法的准确性和简单性.
- * 分数顺序分析和图形表示验证了该技术的有效性.
结论:
- *自然变换分解法是分析分数级非线性微分方程的强大而有效的工具.
- * 该研究验证了该方法对量子场理论和相关科学领域的复杂模型的适用性.
- * 这种方法提供了一种简单可靠的方法来获得近似的分析解决方案.
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