Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives

Abstract

AbstractIn this paper the fractional Euler-Lagrange equation is considered. The fractional equation with the left and right Caputo derivatives of orderα∈ (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.