On the existence of solutions for fractional boundary value problems on the ethane graph

Abstract

Abstract 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.

Keywords

• Boundary value problem
• Fractional differential equation
• Ethane graph
• Caputo derivative