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Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives

Part of:Real functionsGeneral theory in ordinary differential equationsHamiltonian and Lagrangian mechanicsIntegral equations, integral transforms

Published online by Cambridge University Press:  11 October 2016

Tomasz Blaszczyk and
Mariusz Ciesielski
Tomasz Blaszczyk*
Affiliation:
Czestochowa University of Technology, Institute of Mathematics, al. Armii Krajowej 21, 42-201 Czestochowa, Poland
Mariusz Ciesielski*
Affiliation:
Czestochowa University of Technology, Institute of Computer and Information Sciences, ul. Dabrowskiego 73, 42-201 Czestochowa, Poland
*
*Corresponding author. Email:tomasz.blaszczyk@im.pcz.pl (T. Blaszczyk), mariusz.ciesielski@icis.pcz.pl (M. Ciesielski)
*Corresponding author. Email:tomasz.blaszczyk@im.pcz.pl (T. Blaszczyk), mariusz.ciesielski@icis.pcz.pl (M. Ciesielski)

Abstract

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In this paper the fractional Euler-Lagrange equation is considered. The fractional equation with the left and right Caputo derivatives of order α ∈ (0,1] is transformed into its corresponding integral form. Next, we present a numerical solution of the integral form of the considered equation. On the basis of numerical results, the convergence of the proposed method is determined. Examples of numerical solutions of this equation are shown in the final part of this paper.

Keywords

Fractional Euler-Lagrange equationfractional integral equationnumerical solutionCaputo derivatives

MSC classification

Secondary:26A33: Fractional derivatives and integrals34A08: Fractional differential equations65R20: Integral equations70H03: Lagrange's equations

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017, pp. 173 - 185
Copyright
Copyright © Global-Science Press 2017 

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