Existence and Simulation of Solutions for a Class of Fractional Differential Systems with $p$-Laplacian Operators on Star Graphs

Abstract

This paper is mainly concerned with the existence and simulation of solutions for a class of Caputo fractional differential systems with $p$-Laplacian operators on star graphs. The Hyers-Ulam stability of the systems on star graphs is also proved. Furthermore, an example on a formaldehyde graph is presented to demonstrate the practicality of the main results. The innovation of this paper lies in combining a fractional differential system with a formaldehyde graph, interpreting the chemical bonds as the edges of the graph, and exploring the existence and numerical simulation of solutions to the fractional differential system on this unique graph structure.