Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions

Abstract

We introduce a new concept of coupled flux conditions and unify it with nonlocal coupled strip and multi-point boundary conditions. Equipped with the unified boundary conditions, a nonlinear coupled system of Liouville-Caputo type fractional differential equations is studied. Existence and uniqueness results for the given boundary value problem are obtained by applying Banach’s fixed point theorem and Leray–Schauder alternative, and are well illustrated with the aid of examples. Our work is not only new in the given configuration but also yields several new results as its special cases.