This work presents a novel approach to describe spectral properties of graphene layers with well defined edges.We microscopically analyze the boundary problem for the continuous Bogoliubov-de Gennes-Dirac (BdGD) equations and derive the Green functions for normal and superconducting graphene layers.Importing the idea used in tight-binding (TB) models of a microscopic hopping that couples different regions, we are able to set up and solve an algebraic Dyson's equation describing a graphene-superconductor junction.For this coupled system we analytically derive the Green functions and use them to calculate the local density of states and the spatial variation of the induced pairing correlations in the normal region.Signatures of specular Andreev reflections are identified.