Abstract
Few studies have investigated the existence and uniqueness of solutions for fractional differential equations on star graphs until now. The published papers on the topic are based on the assumption of existence of one junction node and some boundary nodes as the origin on a star graph. These structures are special cases and do not cover more general non-star graph structures. In this paper, we state a labeling method for graph vertices, and then we prove the existence results for solutions to a new family of fractional boundary value problems (FBVPs) on the methylpropane graph. We design the chemical compound of the methylpropane graph with vertices specified by 0 or 1, and on every edge of the graph, we consider fractional differential equations. We prove the existence of solutions for the proposed FBVPs by means of the Krasnoselskii’s and Scheafer’s fixed point theorems, and further, we study the Ulam–Hyers type stability for the given multi-dimensional system. Finally, we provide an illustrative example to examine our results.
Highlights
Some natural phenomena throughout the world have been studied using initial and BVPs for many years
There has been some interest in studying mathematical models that are expressed on graphs via ordinary or fractional differential equations, due to their graph representation
This field of mathematics relates graph theory to chemistry, and investigates the chemical changes resulting from interatomic bonds along bond lines and their effects, and these studies are performed in the form of various models of fractional differential equations
Summary
Shahram Rezapour 1,2,† , Chernet Tuge Deressa 3,† , Azhar Hussain 4, *,† , Sina Etemad 1,†.
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