  Fundamental rules and definitions of Fractional Differintegrals are outlined.
Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are
determined. The functions exhibit incident and reflected plane waves as well as
diffracted incident and reflected waves of the half-plane edge. They allow to
construct the Sommerfeld half-plane diffraction solutions. Parabolic-Wave
Equation (PWE, Leontovich-Fock) for paraxial propagation is factorized and
differetial fractional solutions of Fresnel-integral type are derived. We
arrived at two solutions, which are the mothers of known and new solutions.
