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Chemical graph theory is an interdisciplinary mathematics and chemistry discipline that obtains mathematical information about the structure of target compounds and is an important research branch in theoretical pharmacology and nanomedicine. This paper study a coupled Hadamard type sequential fractional differential system on glucose graphs and establishes the Ulam’s stability and existence of the system solutions. Furthermore, we examine examples against different background graphs and provide approximate graphs of the solutions. The novelty of this paper is that the origin of each edge is not fixed in modeling the glucose graphs, and one of the two vertices of the corresponding edge can be arbitrarily chosen as the origin to build the system and give the approximate graphs of the solutions using iterative methods and numerical simulation.

In this paper, we are concerned with the stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations. The existence and uniqueness of the solution of the fractional system are obtained through Schaefer and Banach fixed point theorems, and sufficient conditions for the existence and uniqueness of the solutions are also developed. Subsequently, the Hyers-Ulam stability and generalized Hyers-Ulam stability of the solution are considered. In particular, two examples are given to illustrate the main results. The interesting aspect of this paper is that it performs numerical simulations using the monotone iterative method to verify the applicability of the system.