Existence and stability of solutions for Hadamard type fractional differential systems with $p$-Laplacian operators on benzoic acid graphs

Benzoic acid is mainly used in the preparation of sodium benzoate preservatives, as well as in the synthesis of drugs and dyes. Therefore, a thorough understanding of its properties is of utmost importance. This paper is mainly concerned with the existence of solutions for a class of Hadamard type fractional differential systems with $p$-Laplacian operators on benzoic acid graphs. Meanwhile, the Hyers-Ulam stability of the systems is also proved. Furthermore, an example is presented on a formaldehyde graph to demonstrate the applicability of the conclusions obtained. The novelty of this paper lies in the integration of fractional differential equations with graph theory, utilizing the formaldehyde graph as a specific case for numerical simulation, and providing an approximate solution graph after iterations.