This paper establishes a rigorous analysis of a coupled hybrid fractional differential system involving a generalized Hilfer operator under integral and antiperiodic boundary conditions. The existence and uniqueness of solutions are proved using Dhage’s fixed point theorem for existence and the Banach contraction principle for uniqueness. Furthermore, we establish Ulam–Hyers stability by deriving the following explicit and computable bound estimate: ∥u^−u∥∥v^−v∥≤ (I−χ) −1C1ϵ1C2ϵ2, where C1 and C2 are positive constants depending on the system parameters, ϵ1, ϵ2 denote the perturbation bounds, and χ is the associated Lipschitz matrix. This formulation provides a more detailed stability description than scalar criteria, as it captures the interactions among the system components through the entries of χ, leading to a more informative stability estimate. Two illustrative examples confirm the theoretical results and demonstrate their potential applicability for modeling real-world phenomena where memory effects are present.
Lachouri et al. (Thu,) studied this question.