The Fractionary Schr\"{o}dinger Equation, Green Functions and Ultradistributions

In this work, we generalize previous results about the Fractionary Schr"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate the Green’s function for a free particle in the general case, for an arbitrary order of the derivative index.