Fractional derivative analysis of Helmholtz and paraxial-wave equations

Turski, A. J.; Atamaniuk, B.; Turska, E.

Artykuł - szczegóły

Tytuł artykułu

Fractional derivative analysis of Helmholtz and paraxial-wave equations

Autorzy

Turski A. J. , Atamaniuk B. , Turska E.

Identyfikatory

Warianty tytułu

Języki publikacji

Abstrakty

Fundamental rules and definitions of Fractional Calculus are outlined. Factorizing 1-D and 2-D Helmholtz equations, four semi-differential eigenfunctions are determined. The functions exhibit incident and reHected plane waves as well as diffracted incident and reflected waves on 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 differential fractional solutions of Fresnel-integral type are determined. We arrived at two solutions, which are the mothers of known and new solutions.

Słowa kluczowe

Helmholz equation Helmholz wave equation parabolic equation fractional calculus wave propagation differential fractional solution calculus

równanie Helmholza równanie falowe Helmholza równanie paraboliczne rachunek ułamkowy rachunek

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

Journal of Technical Physics

Rocznik

2003

Tom

Vol. 44, no 2

Strony

193--206

Opis fizyczny

Bibliogr. 25 poz., wykr.

Twórcy

autor

Turski A. J.

Department of Theory of Continuous Media Institute of Fundamental Technological Research, PAS ul. Świętokrzyska 21, 00-049 Warsaw, Poland

autor

Atamaniuk B.

Department of Theory of Continuous Media Institute of Fundamental Technological Research, PAS ul. Świętokrzyska 21, 00-049 Warsaw, Poland

autor

Turska E.

Department of Theory of Continuous Media Institute of Fundamental Technological Research, PAS ul. Świętokrzyska 21, 00-049 Warsaw, Poland

Bibliografia

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Bibliografia

Identyfikator YADDA

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