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Volume 9, Issue 1
Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives

Tomasz Blaszczyk & Mariusz Ciesielski

DOI: 10.4208/aamm.2015.m970

Adv. Appl. Math. Mech., 9 (2017), pp. 173-185.

Published online: 2018-05

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  • 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.

  • Keywords

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

  • AMS Subject Headings

26A33, 34A08, 65R20, 70H03

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-173, author = {Blaszczyk , Tomasz and Ciesielski , Mariusz}, title = {Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m970}, url = {http://global-sci.org/intro/article_detail/aamm/12143.html} }
TY - JOUR T1 - Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives AU - Blaszczyk , Tomasz AU - Ciesielski , Mariusz JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 173 EP - 185 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m970 UR - https://global-sci.org/intro/article_detail/aamm/12143.html KW - Fractional Euler-Lagrange equation, fractional integral equation, numerical solution, Caputo derivatives. AB -

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.

Blaszczyk , Tomasz and Ciesielski , Mariusz. (2018). Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives. Advances in Applied Mathematics and Mechanics. 9 (1). 173-185. doi:10.4208/aamm.2015.m970
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