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

Siedlecki Jarosław

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 4

112--119

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.