The novel existence results of solutions for a nonlinear fractional boundary value problem on the ethane graph
Ali Turab, Wutiphol Sintunavarat
Abstract
Chemical graph theory is a branch of mathematics that combines graph theory and chemistry and discusses the effect of research on “serious” or “pure” mathematics. A range of new graph ideas can be identified in the current development of mathematical chemistry and chemical graph theory. These advances include chemical kinetics as well as biomacromolecules. On star graphs, a few researchers have studied fractional differential equations. They used star graphs because their approach requires a common point that has edges with other nodes, whereas there are no edges between them. Our aim is to broaden the approach by using the idea of an ethane graph, which is an organic chemical compound with the chemical formula C2H6 and having more than one junction nodes. In this work, we analyze the existence of solutions on such graphs for the fractional boundary value problem in the sense of Caputo fractional derivative. Inspired by a graph describing ethane’s chemical compound, we assume a graph with labeled vertices of 0 or 1 and describe fractional differential equations on each edge of this graph. We use the notable fixed point theorems to find the existence and uniqueness of a solution to the proposed fractional differential equation. An example is also presented to support our main results.