Fractional Euler-Lagrange equations revisited

Abstract

This paper presents the necessary and sufficient optimality conditions for the Euler-Lagrange fractional equations of fractional variational problems with determining in which spaces the functional must exist where the functional contains right and left fractional derivatives in the Riemann-Liouville sense and the upper bound of integration less than the upper bound of the interval of the fractional derivative. In order to illustrate our results, one example is presented.