A few researchers have studied fractional differential equations on star graphs. They use star graphs because their method needs a common point which has edges with other nodes while other nodes have no edges between themselves. It is natural that we feel that this method is incomplete. Our aim is extending the method on more generalized graphs. In this work, we investigate the existence of solutions for some fractional boundary value problems on the ethane graph. In this way, we consider a graph with labeled vertices by 0 or 1, inspired by a graph representation of the chemical compound of ethane, and define fractional differential equations on each edge of this graph. Also, we provide an example to illustrate our last main result.

一些研究人员研究了星图上的分数阶微分方程。他们之所以使用星形图，是因为他们的方法需要一个公共点，该公共点与其他节点具有边，而其他节点之间没有边。很自然，我们认为此方法不完整。我们的目标是将该方法扩展到更广义的图上。在这项工作中，我们研究了乙烷图上某些分数边值问题的解的存在性。通过这种方式，我们考虑到一个以0或1标记顶点的图形，该图形受到乙烷化学化合物图形表示的启发，并在该图形的每个边上定义了分数阶微分方程。另外，我们提供一个示例来说明我们的最后一个主要结果。