Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani, Thailand.
PLoS One. 2022 Aug 12;17(8):e0270148. doi: 10.1371/journal.pone.0270148. eCollection 2022.
A theory of chemical graphs is a part of mathematical chemistry concerned with the effects of connectedness in chemical graphs. Several researchers have studied the solutions of fractional differential equations using the concept of star graphs. They employed star graphs because their technique requires a central node with links to adjacent vertices but no edges between nodes. The purpose of this paper is to extend the method's range by introducing the concept of an octane graph, which is an essential organic compound having the formula C8H18. In this manner, we analyze a graph with vertices annotated by 0 or 1, which is influenced by the structure of the chemical substance octane, and formulate a fractional boundary value problem on each of the graph's edges. We use the Schaefer and Krasnoselskii fixed point theorems to investigate the existence of solutions to the presented boundary value problems in the framework of the Caputo fractional derivative. Finally, two examples are provided to highlight the importance of our results in this area of study.
化学图论是数学化学的一个分支，主要研究化学图中连通性的影响。一些研究人员使用星形图的概念研究分数阶微分方程的解。他们选择星形图是因为他们的技术需要一个中央节点，该节点与相邻顶点有链接，但节点之间没有边。本文的目的是通过引入辛烷图的概念来扩展该方法的范围，辛烷图是一种具有化学式 C8H18 的基本有机化合物。通过这种方式，我们分析了一个顶点标记为 0 或 1 的图，该图受到化学物质辛烷结构的影响，并在每个图的边上制定了分数阶边值问题。我们使用 Schaefer 和 Krasnoselskii 不动点定理，在 Caputo 分数阶导数的框架下研究所提出的边值问题解的存在性。最后，提供了两个例子来说明我们在该研究领域的结果的重要性。
