dorsal/arxiv
View SchemaFractional Derivative Analysis of Helmholtz and Paraxial-Wave Equations
| Authors | A. J. Turski, B. Atamaniuk, E. Turska |
|---|---|
| Categories | |
| ArXiv ID | physics/0203047 |
| URL | https://arxiv.org/abs/physics/0203047 |
Abstract
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.
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"abstract": "Fundamental rules and definitions of Fractional Differintegrals are outlined.\nFactorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are\ndetermined. The functions exhibit incident and reflected plane waves as well as\ndiffracted incident and reflected waves of the half-plane edge. They allow to\nconstruct the Sommerfeld half-plane diffraction solutions. Parabolic-Wave\nEquation (PWE, Leontovich-Fock) for paraxial propagation is factorized and\ndifferetial fractional solutions of Fresnel-integral type are derived. We\narrived at two solutions, which are the mothers of known and new solutions.",
"arxiv_id": "physics/0203047",
"authors": [
"A. J. Turski",
"B. Atamaniuk",
"E. Turska"
],
"categories": [
"physics.optics"
],
"title": "Fractional Derivative Analysis of Helmholtz and Paraxial-Wave Equations",
"url": "https://arxiv.org/abs/physics/0203047"
},
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