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 realworld 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.