Nonlinear Sequential Fractional Integro-Differential Systems: Caputo-Type Derivatives and Boundary Constraints

In recent years, the study of sequential fractional differential equations (SFDEs) has become increasingly important in multiple domains of science and engineering. This work investigates a new class of boundary value problems (BVPs) characterized by nonlocal closed boundary conditions involving SFDEs with Caputo fractional integral operators. The existence of solutions is established using the Leray–Schauder alternative, while the uniqueness is demonstrated through the Banach fixed point theorem. To illustrate the main findings, several examples are presented, along with a discussion of specific cases that arise from the analysis.