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Numerical solution of fractional Euler-Lagrange equation with multipoint boundary conditions

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Języki publikacji
EN
Abstrakty
EN
In this paper we consider an ordinary fractional differential equation containing a composition of left and right fractional derivatives. This type of equation is known in literature as the boundary conditions. We proposed a numerical scheme using the finite difference method. In the final part of the paper, examples of the solutions are shown.
Rocznik
Strony
43--48
Opis fizyczny
Bibliogr. 15 poz., rys., tab.
Twórcy
Bibliografia
  • [1] Agrawal O.P., Formulation of Euler-Lagrange equations for fractional variational problems, J. Math. Anal. Appl. 2002, 272, 368-379.
  • [2] Agrawal O.P., Generalized variational problems and Euler-Lagrange equations, Comput. Math. Appl. 2010, 59, 1852-1864.
  • [3] Baleanu D., Trujillo D.J.J., On exact solutions of a class of fractional Euler-Lagrange equations, Nonlinear Dyn. 2008, 52, 331-335.
  • [4] Klimek M., Lagrangean and Hamiltonian fractional sequential mechanics, Czech. J. Phys. 2002, 52, 1247-1253.
  • [5] 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.
  • [6] Klimek M., On Solutions of Linear Fractional Differential Equations of a Variational Type, The Publishing Office of the Czestochowa University of Technology, Czestochowa 2009.
  • [7] Riewe F., Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev. E 1996, 53, 1890-1899.
  • [8] Hilfer R., Applications of Fractional Calculus in Physics, World Scientific, Singapore 2000.
  • [9] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam 2006.
  • [10] Leszczynski J.S., Blaszczyk T., Modeling the transition between stable and unstable operation while emptying a silo, Granular Matter 2011, 13, 429-438.
  • [11] Sommacal L., Melchior P., Cabelguen J.M., Ostaloup A., Ijepeert A., Fractional multimodels of the gastrocnemius muscle for tetanus pattern, [in:] J. Sabatier, O.P. Agrawal, J.A.T. Machado, Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering, Springer-Verlag, 2007, 271-285.
  • [12] Blaszczyk T., Ciesielski M., Fractional Euler-Lagrange equations-numerical solutions and applications of reflection operator, Scientific Research of the Institute of Mathematics and Computer Science 2010, 2(9), 17-24.
  • [13] Blaszczyk T., Application of the Rayleigh-Ritz method for solving fractional oscillator equation, Scientific Research of the Institute of Mathematics and Computer Science 2009, 2(8), 29-36.
  • [14] Blaszczyk T., Ciesielski M., Klimek M., Leszczynski J., Numerical solution of fractional oscillator equation, Applied Mathematics and Computation 2011, 218, 2480-2488.
  • [15] Oldham K.B., Spanier J., The fractional calculus. Theory and applications of differentiation and integration to arbitrary order, Academic Press, New York 1974.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPC6-0016-0005
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