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 - <p style="text-align: justify;">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.</p>