谢胡变换与其他众所周知的变换的二元性以及对分数顺序微分方程的应用
Nabil Mlaiki1, Noor Jamal2, Muhammad Sarwar1,2
1Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
PloS one
|April 29, 2025
概括
研究人员探索了谢胡变换与拉普拉斯和里埃等其他积分变换之间的二元关系. 这些连接简化了解决复杂的微分方程和小数方程,节省了宝贵的研究时间.
科学领域:
- 数学 数学 是一个数学.
- 应用科学 应用科学
- 工程 工程师 工程师 工程师
背景情况:
- 整体转换是应用科学和工程学的关键工具.
- 研究人员经常面临应用特定变换到微分方程和积分方程的挑战.
- 谢胡变换通过调整参数来表现出对其他已知的积分变换的收性质.
研究的目的:
- 要推导出Shehu变换与其他几个积分变换之间的相互转换 (二元) 关系.
- 建立一个框架来简化在问题解决中应用积分变换的方法.
- 突出这些二元关系在应对复杂的数学挑战中的实用性.
主要方法:
- 谢胡变换与自然,苏穆杜,拉普拉斯,拉普拉斯-卡森,富里埃,阿布德,埃尔扎基,卡马尔和梅林变换之间的二元关系的推导.
- 分析这些新衍生关系的属性和含义.
- 使用这些相互转换属性来轻松解决微分方程的演示.
主要成果:
- 建立了全面的二元关系,将Shehu变换与其他多个整体变换连接起来.
- 证明这些关系简化了解决微分方程和积分方程的过程,特别是当直接应用变换时是复杂的.
- 展示了在解决分数顺序微分方程中更容易可视化和应用的潜力.
结论:
- 由此产生的二元关系为研究人员提供了显著的优势,因为它简化了复杂的数学问题.
- 这些关系提高了各种积分变换的适用性和易用性,包括Shehu变换.
- 这些发现有助于更有效地解决应用数学,科学和工程方面的问题,特别是对于微积分计算.
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