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Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives

Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives
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Year:    2017

Author:    Tomasz Blaszczyk, Mariusz Ciesielski

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 173–185

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2015.m970

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 173–185

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Fractional Euler-Lagrange equation fractional integral equation numerical solution Caputo derivatives.

Author Details

Tomasz Blaszczyk

Mariusz Ciesielski

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