Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and Integrals

In this article, we investigate the existence and uniqueness of solutions for a nonlinear coupled system of Liouville–Caputo type fractional integro-differential equations supplemented with non-local discrete and integral boundary conditions. The nonlinearity relies both on the unknown functions and their fractional derivatives and integrals in the lower order. The consequence of existence is obtained utilizing the alternative of Leray–Schauder, while the result of uniqueness is based on the concept of Banach contraction mapping. We introduced the concept of unification in the present work with varying parameters of the multi-point and classical integral boundary conditions. With the help of examples, the main results are well demonstrated.