Existence of a weak solution for fractional Euler-Lagrange equations

We derive sufficient conditions ensuring the existence of a weak solution u for fractional Euler-Lagrange equations of the type: partial derivative L/partial derivative x (u, D(-)(alpha)u, t) + D-+(alpha) (partial derivative L/partial derivative y (u, D(-)(alpha)u, t)) = 0, (EL alpha) on a real interval [a, b] and where D--(alpha) and D-+(alpha) are the fractional derivatives of Riemann-Liouville of order 0 < alpha < 1. (C) 2012 Elsevier Inc. All rights reserved.