通过一般化的卡普托-阿坦加纳-巴莱努衍生物对分数朗格文-斯图尔姆-利乌维尔问题得到有效的结果
Sabri T M Thabet1,2,3, Abdelatif Boutiara4, Mohammad Esmael Samei5
1Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu, India.
PloS one
|October 2, 2024
概括
这项研究探讨了用卡普托-阿坦加纳-巴莱努分数导数的概括的朗格温-斯图尔姆-利乌维尔微分方程. 它证明了这些复杂的分数微分问题的存在,独特性和稳定性标准.
科学领域:
- 分数微积分的计算.
- 微分方程 微分方程 微分方程
- 非线性分析 非线性分析
背景情况:
- 一般化的兰格温-斯图尔姆-利乌维尔问题对于模拟各种物理现象至关重要.
- 高阶的卡普托-阿坦加纳-巴莱努分数衍生品提供了先进的建模能力.
- 了解解决方案的存在,独特性和稳定性是至关重要的.
研究的目的:
- 为了研究更高阶的卡普托-阿坦加纳-巴莱努分数导数的概括的朗格温-斯图尔姆-利乌维尔微分问题.
- 用固定点定理来确定解决方案的存在和独特性.
- 为拟议的分数模型分析各种Ulam-Hyers稳定性标准.
主要方法:
- 应用克兰斯诺塞尔斯基和巴纳赫的固定点定理.
- 使用非线性分析技术.
- 结合Caputo-Atangana-Baleanu高阶的微积分计算,对一个正增函数 ρ.
主要成果:
- 解决方案的存在和独特性通过固定点定理来证明.
- 对Ulam-Hyers,一般化的Ulam-Hyers,Ulam-Hyers-Rassias和一般化的Ulam-Hyers-Rassias稳定性的全面分析.
- 理论发现通过说明性示例,表格和图形来验证.
结论:
- 这项研究成功地建立了一个分数微分方程等级的理论框架.
- 这些发现有助于理解由微积分计算建模的复杂动态系统.
- 严格的分析为进一步研究分数微分方程及其应用提供了基础.
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