In this paper, the existence and uniqueness of the solutions to impulsive coupled system of fractional differential equations with Caputo-Hadamard are investigated. Furthermore, Ulam's type stability of the proposed coupled system is studied. The approach is based on a Perov type fixed point theorem for contractions.

<abstract><p>This paper discusses the existence, uniqueness and stability of solutions for a nonlinear fractional differential system consisting of a nonlinear Caputo-Hadamard fractional initial value problem (FIVP). By using some properties of the modified Laplace transform, we derive an equivalent Hadamard integral equation with respect to one-parametric and two-parametric Mittag-Leffer functions. The Banach contraction principle is used to give the existence of the corresponding solution and its uniqueness. Then, based on a Lyapunov-like function and a $ \mathcal{K} $-class function, the generalized Mittag-Leffler stability is discussed to solve a nonlinear Caputo-Hadamard FIVP. The findings are validated by giving an example.</p></abstract>