An approximation of the analytical solution of the fractional Euler-Lagrange equation

• Autorzy: Ciesielski M. , Błaszczyk T.
• Języki publikacji: EN

Abstrakty

EN

In this paper the fractional Euler-Lagrange equation of order α ∈ (0, 1] in the finite time interval is considered. This equation is transformed to the integral form by the use of the fractional integral operators. Next, the numerical approximation of the analytical solution is presented. Finally, some examples of numerical solutions are presented.

Słowa kluczowe

EN

fractional Euler-Lagrange equation; numerical solution

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 4
• Strony: 23--30
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Ciesielski M.

• Institute of Computer and Information Sciences, Czestochowa University of Technology

autor

Błaszczyk T.

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

Bibliografia

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• [2] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam 2006.
• [3] Podlubny I., Fractional Differential Equations, Academic Press, San Diego 1999.
• [4] Baleanu D., Trujillo J.J., On exact solutions of a class of fractional Euler-Lagrange equations, Nonlinear Dyn. 2008, 52, 331-335.
• [5] Klimek M., On Solutions of Linear Fractional Differential Equations of a Variational Type, The Publishing Office of the Czestochowa University of Technology, Czestochowa 2009.
• [6] Agrawal O.P., Hasan M.M., Tangpong X.W., A numerical scheme for a class of parametric problem of fractional variational calculus, J. Comput. Nonlinear Dyn. 2012, 7, 021005, 6pp.
• [7] Blaszczyk T., Ciesielski M., Klimek M., Leszczynski J., Numerical solution of fractional oscillator equation, Applied Mathematics and Computation 2011, 218, 2480-2488.
• [8] Lotfi A., Yousefi S.A., A numerical technique for solving a class of fractional variational problems, Journal of Computational and Applied Mathematics 2013, 237(1), 633-643.
• [9] 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.