Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives (Advances in Applied Mathematics and Mechanics, 2018)
In this paper the fractional Euler-Lagrange equation is considered. The fractionalequation with the left and right Caputo derivatives of order α ∈ (0,1] is transformedinto its corresponding integral form. Next, we present a numerical solutionof the integral form of the considered equation. On the basis of numerical results, theconvergence of the proposed method is determined. Examples of numerical solutionsof this equation are shown in the final part of this paper.