On a nonlinear coupled Caputo-type fractional differential system with coupled closed boundary conditions

Abstract

<abstract><p>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.</p></abstract>