We introduce a novel notion of coupled closed boundary conditions and investigate a nonlinear system of Caputo fractional differential equations equipped with these conditions. The existence result for the given problem is proved via the Leray-Schauder alternative, while the uniqueness of its solutions is accomplished by applying the Banach fixed point theorem. Examples are constructed for the illustration of the main results. Some special cases arising from the present study are discussed.

In this paper, we introduce a new class of nonlocal multipoint-integral boundary conditions with respect to the sum and difference of the governing functions and analyze a coupled system of nonlinear Caputo fractional differential equations equipped with these conditions. The existence and uniqueness results for the given problem are proved via the tools of the fixed point theory. We also discuss the case of nonlinear Riemann-Liouville integral boundary conditions. The obtained results are well-illustrated with examples.

This paper is concerned with the study of a new class of boundary value problems involving a right Caputo fractional derivative and mixed Riemann-Liouville fractional integral operators, and a nonlocal multipoint version of the closed boundary conditions. The proposed problem contains the usual and mixed Riemann-Liouville integrals type nonlinearities. We obtain the existence and uniqueness results with the aid of the fixed point theorems. Examples are presented for illustrating the abstract results. Our results are not only new in the given configuration but also specialize to some interesting situations.