Existence, Uniqueness and Continuous Dependence of Solutions for a Noncontractive Caputo Fractional Delay Equation

This study establishes a complete qualitative analysis for a class of noncon-tractive Caputo fractional delay differential equations subject to integral boundary conditions. First, the existence of solutions is proved under mild assumptions using Sadovskii’s fixed point theorem, with the noncontractive property explicitly characterized by the derived condition k_op. Uniqueness is then established via an innovative application of the fractional Grön-wall inequality. Furthermore, a rigorous perturbation framework is developed to prove the continuous dependence of solutions on external parameters, ensuring structural robustness. The theoretical results are validated both analytically and through numerical simulations in MATLAB, which illustrate the system’s distinct dynamical behavior across fractional orders α ∈ (0, 1), highlighting enhanced memory effects at lower orders and transitional dynamics at intermediate values. Our results improve, extend and provide a comprehensive analytical foundation for noncontractive fractional delay systems and contribute significantly to the qualitative theory of fractional differential equations with applications in hereditary and memory-dependent processes, as described in the literature.