稳定性分析和分数边界值问题的解决方案在循环西兰图上
Guotao Wang1, Hualei Yuan1, Dumitru Baleanu2,3
1School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030031, China.
Heliyon
|July 8, 2024
概括
本研究使用固定点定理分析了循环西兰图的分数符合边界值问题. 它证实了解决方案的存在和稳定性,为分子结构建模提供了洞察力.
科学领域:
- 图形理论 图形理论
- 数学化学 数学化学
- 分数微积分的微积分计算
背景情况:
- 赛克洛西兰的分子结构是用0或1标记的顶点图形来建模的.
- 分数符合性边界值问题在各种科学和工程领域至关重要.
- 固定点定理是分析微分方程解决方案存在的基本工具.
研究的目的:
- 在循环西兰图上调查分数符合边界值问题的解决方案的存在.
- 分析所考虑问题的不同类型的乌拉姆稳定性.
- 为获得的结果提供一个支持的例子.
主要方法:
- 施舍弗和克拉斯诺塞尔斯基固定点定理的应用.
- 对乌拉姆-海尔斯稳定性,概括的乌拉姆-海尔斯稳定性,乌拉姆-海尔斯-拉西亚斯稳定性和概括的乌拉姆-海尔斯-拉西亚斯稳定性的分析.
- 使用一个图形模型,灵感来自于cyclopentasilane的分子结构.
主要成果:
- 确定了循环西兰图上的分数符合边界值问题的解决方案的存在.
- 研究了各种形式的Ulam稳定性 (Ulam-Hyers,一般化的Ulam-Hyers,Ulam-Hyers-Rassias,一般化的Ulam-Hyers-Rassias).
- 提出了一个具体的例子来验证理论发现.
结论:
- 该研究成功地证明了在环西兰图上对分数符合边界值问题的解决方案的存在和稳定性.
- 这些发现有助于对分子结构和分数计算应用的数学理解.
- 提供的示例加强了理论结果的意义和适用性.
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