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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.

Existence and simulation of solutions for a class of fractional differential systems with p-Laplacian operators on star graphs

“…Zhang et al [19] added a function λ i (x) on the basis of the reference [17], and proved the existence result by the fixed point theorem. In addition, Nan [20] discussed the existence of a coupled fractional differential system on a glucose graph and proved the Hyers-Ulam stability of solutions to the system. It can be seen that in literatures [17][18][19], attention was mainly focused on the existence of solutions to the fractional differential systems, while Nan et al [20,21] conducted numerical simulations without combining traditional star graphs.…”

“…Inspired by the above references [17][18][19][20][21][22], we study the existence and Hyers-Ulam stability of the solution to the boundary value problem with p-Laplacian operator on star graphs as follows…”

Stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations

“…By numerically simulating the solution of the equation, we are able to solve problems in economics more clearly and accurately. However, numerical simulation has been rarely used to describe the solutions of coupled systems as well as Hyers-Ulam stability [37][38][39].…”