Application of the Rayleigh-Ritz method for solving fractional oscillator equation

• Autorzy: Błaszczyk T.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fractional oscillator equation; Rayleigh-Ritz method

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2009
• Tom: Vol. 8, nr 2
• Strony: 29--36
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Błaszczyk T.

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

Bibliografia

• [1] Riewe F., Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev. E 1996, 53, 1890-1899.
• [2] Riewe F., Mechanics with fractional derivatives, Phys. Rev. E 1997, 55, 3581-3592.
• [3] Agrawal O.P., Formulation of Euler-Lagrange equations for fractional variational problems, J. Math. Anal. Appl. 2002, 272, 368-379.
• [4] Agrawal O.P., A general formulation and solution scheme for fractional optimal control problems, Nonlinear Dyn. 2004, 38, 323-337.
• [5] Baleanu D., Avkar T., Lagrangians with linear velocities within Riemann-Liouville fractional derivatives, Nuovo Ciemnto B 2004, 119, 73-79.
• [6] Baleanu D., Muslish S.I., Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives, Phys. Scr. 2005, 72, 119-121.
• [7] Baleanu D., Fractional Hamiltonian analysis of irregular systems, Signal Process 2006, 86, 2632-2636.
• [8] Cresson J., Fractional embedding of differential operators and Lagrangian systems, J. Math. Phys. 2007, 48, 033504.
• [9] Klimek M., Fractional sequential mechanics – models with symmetric fractional derivative, Czech. J. Phys. 2001, 51, 1348-1354.
• [10] Klimek M., Lagrangean and Hamiltonian fractional sequential mechanics, Czech. J. Phys. 2002, 52, 1247-1253.
• [11] Agrawal O.P., Analytical schemes for a new class of fractional differential equations, J. Phys. A: Mathematical and Theoretical 2007, 40, 21, 5469-5477.
• [12] Baleanu D., Trujillo J.J., On exact solutions of a class of fractional Euler-Lagrange equations, Nonlinear Dyn. 2008, 52, 331-335.
• [13] Klimek M., Solutions of Euler-Lagrange equations in fractional mechanics, AIP Conference Proceedings 956. XXVI Workshop on Geometrical Methods in Physics, Eds. P. Kielanowski, A. Odzijewicz, M. Schlichenmaier, T. Voronov, Białowieża 2007, 73-78.
• [14] Klimek M., G-Meijer functions series as solutions for certain fractional variational problem on a finite time interval, Journal Europeen des Systemes Automatises (JESA) 2008, 42, 653-664.
• [15] Agrawal O.P., A numerical scheme and an error analysis for a class of Fractional Optimal Control problems, Proceedings of the 7th International Conference on Multibody Systems, Nonlinear Dynamics and Control, San Diego, California, USA 2009.
• [16] Lord Rayleigh, The Theory of Sound, Volume 1, The Macmillan Company, New York 1877 (reprinted 1945 by Dover Publications).
• [17] Ritz W., Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik, Journal für die Reine und Angewandte Mathematik 1908, 135, 1-61.
• [18] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam 2006.