On Sequential Coupled Caputo-Type Fractional Differential Inclusions with Coupled Boundary Conditions: A Multivalued Fixed-Point Approach

This study addresses the existence of solutions for a class of coupled fractional differential inclusions subject to coupled boundary conditions. The analysis is developed within the framework of nonlinear functional analysis by employing Carathéodory-type assumptions, the Leray–Schauder nonlinear alternative, and the Covitz–Nadler fixed-point theorem for multivalued mappings. The proposed approach accommodates both convex and non-convex set-valued nonlinearities, thereby broadening the scope of the results. Under suitable restrictions on the problem parameters, several corollaries are established as direct consequences of the main findings. An example is included to demonstrate the practical applicability and validity of the theoretical results.