This paper develops an operator-reduction framework for a class of coupled implicit Caputo-Hadamard fractional differential systems subject to nonlocal Hadamard integral constraints. The system, involving fractional derivatives in both state and auxiliary variables, is resolved through a pointwise contraction argument that eliminates the auxiliary components and reduces the problem to a two-dimensional fixed-point operator acting on a Banach space of continuous functions. This reduction overcomes the compactness obstruction that arises in direct multi-component formulations. Under explicit growth and smallness conditions, the existence of at least one solution is established via Mönch’s fixed-point theorem. By imposing strengthened Lipschitz hypotheses, the reduced operator becomes a strict contraction on an invariant ball, yielding uniqueness and Ulam-Hyers stability with explicit constant CUH=1/(1−Λ). A fully computed example demonstrates the verifiability of the theoretical assumptions and illustrates how the smallness condition Λ<1 governs both existence and stability. The results establish a systematic operator-based approach for implicit Caputo-Hadamard systems with nonlocal integral constraints.
Awadalla et al. (Mon,) studied this question.