Junping Nan, Weimin Hu, Youhui Su, and Xiaoling Han
Stability and Existence of Solutions For Fractional Differential System With p-Laplacian Operator on Star Graphs
Dynamic Systems and Applications 31 (2022) 133-172

https://doi.org/10.46719/dsa202231.03.01

ABSTRACT.
As we all know, star graphs are very useful in physics, chemistry, biology and other fields, but few people have studied the existence of solutions to differential system on star graphs. In this paper, we investigate the existence of solutions to a fractional differential system on star graphs with p-Laplacian operator. Ulam’s stability and existence of the solutions to the fractional differential system on star graphs are proved. In addition, two examples under different background graphs (star graphs and formaldehyde graphs) and the approximation graphics for the solutions are provided to illustrate the application of our main results. The interesting point of this article is that it not only studies the existence of solutions to fractional differential system on the star graphs, but also gives approximate graphs of solutions by using the iterative methods and numerical simulation.

AMS (MOS) Subject Classification. 34B15, 34B45.

Key Words and Phrases. Fractional differential system, star graphs, the fixed point theorems,
Ulam’s stability, numerical simulation.