Abstract
In this paper, we propose a generalized Gronwall inequality in the context of the psi-Hilfer proportional fractional derivative. Using Picard's successive approximation and the definition of Mittag-Leffler functions, we construct the representation formula of the solution for the psi-Hilfer proportional fractional differential equation with constant coefficient in the form of the Mittag-Leffler kernel. The uniqueness result is proved by using Banach's fixed-point theorem with some properties of the Mittag-Leffler kernel. Additionally, Ulam-Hyers-Mittag-Leffler stability results are analyzed. Finally, numerical examples are provided to demonstrate the theory's application.