Existence of Solutions to Fractional Differential Inclusions with Non-Separated and Multipoint Boundary Constraints

A novel and generalized class of fractional differential inclusions has been investigated under a combination of nonlocal, non-separated, multipoint, and integral boundary conditions. Fractional derivatives have been employed to capture memory effects and enhance the modeling accuracy of real-world phenomena. Uncertainty has been addressed through the formulation of set-valued differential inclusions. The proposed boundary conditions have been designed to encompass a wide spectrum of both local and nonlocal types previously reported in the literature. The existence of solutions has been established via the Bohnenblust–Karlin fixed-point theorem. The applicability and effectiveness of the main results have been demonstrated through concrete examples.