Analytical results on coupled Caputo systems with boundary nonlocality and Ulam-Hyers stability

In this paper, we study a coupled system of sequential Caputo fractional differential equations with different fractional orders subject to mixed nonlocal boundary conditions. By transforming the problem into an equivalent system of fractional integral equations, we construct an associated operator in a suitable Banach space framework. Using Banach’s contraction principle and the Leray–Schauder nonlinear alternative, sufficient conditions guaranteeing the existence and uniqueness of solutions are established. In addition, the Ulam–Hyers stability of the considered system is investigated, providing quantitative estimates describing the robustness of the solutions under small perturbations of the governing equations. An illustrative example is presented to verify the theoretical assumptions and demonstrate the applicability of the main results. The obtained results contribute to the qualitative theory of fractional differential systems involving sequential derivatives and nonlocal boundary conditions.