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• W814756876 abstract "In this work a fractional oscillator equation is considered. This type of equation includes a composition of left and right fractional derivatives. A scheme based on the variational Rayleigh-Ritz method is proposed to obtain a numerical solution of the problem. Introduction Fractional oscillator equation is a type of equation which includes a composition of left and right fractional derivatives. This type of equations appears in theoretical fractional mechanics while using the minimum action principle and fractional integration by parts rule. Riewe [1, 2] was the first author who used this method in derivation of fractional differential equations in mechanics. Later sequential Lagrangian and Hamiltonian approaches to the problem were proposed (see for example, [3-10]). Using the fixed point theorems [11-13] one can obtain analytical results. Unfortunately, this solution is represented by series of alternately left and right fractional integrals and therefore is difficult in any practical calculations. In order to generate analytical solution Klimek in [14] shows an application of the Mellin transform, but this solution is represented by complicated series of special functions. Analytical results obtained so far are inspiration to look for approximate solutions. In [15] some approximate solutions based on Fractional Power Series, for a class of Fractional Optimal Control problems is presented. In this paper a numerical scheme based on Rayleigh-Ritz method [16, 17] for fractional oscillator equation is proposed. 1. Basic definitions and formulation of the problem We recall some definitions of the fractional operators [18]: – left fractional Riemann-Liouville integral: ( ) ( ) ( ) ( ) 0 1 0 1 : 0 t f s I f t ds t t s α α α + − = > Γ − ∫ (1) Please cite this article as: Tomasz Blaszczyk, Application of the Rayleigh-Ritz method for solving fractional oscillator equation, Scientific Research of the Institute of Mathematics and Computer Science, 2009, Volume 8, Issue 2, pages 29-36. The website: http://www.amcm.pcz.pl/" @default.
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• W814756876 date "2009-01-01" @default.
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• W814756876 title "An application of the Rayleigh-Ritz method for solving fractional oscillator equation" @default.
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