The manuscript is subdivided into four chapters in addition to an introduction containing a fairlybrief presentation and bibliographical review of the work already undertaken on the topic ad-dressed. A plan of the manuscript is also inserted. In the first chapter, we present some necessaryconcepts related to the half-group theory, which we will use in the second and third chapters. Thesecond chapter deal with a coupled system of differential equations with nonlocal conditions. Wereduce the problem posed to an abstract first-order differential equation, whose coeficient near thederivative is a...