Solution of the harmonic oscillator equation in cylindrical coordinates with fractional boundary conditions

• Autorzy: Siedlecki Jarosław

Identyfikatory

DOI

10.17512/jamcm.2024.4.10

• Języki publikacji: EN

Abstrakty

EN

The boundary value problem consisting of homogeneous second-order ordinarydifferential equation and the classical and/or fractional boundary conditions is considered.Such an equation can describe the motion of the harmonic oscillator in the one-dimensional cylindrical coordinate. The general solution of this equation includes the Bessel functions of the first and second kinds. The particular solutions of the equation are determined on the basis of various constructions of boundary conditions that, in particular, take into account the left- and right-side fractional derivatives defined in the Riemann-Liouville sense. Also, three illustrative examples of particular solutions on the plots are shown.

Słowa kluczowe

EN

fractional calculus; ordinary boundary value problem; differential equation; harmonic oscillator

PL

rachunek ułamkowy; zwykły problem brzegowy; równanie różniczkowe; oscylator harmoniczny

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 4
• Strony: 112--119
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Siedlecki Jarosław

• Department of Mathematics, Czestochowa University of Technology, Czestochowa, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).