Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (α, β)

We derive Euler-Lagrange-type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann-Liouville derivatives of order (alpha, beta), alpha > 0, beta > 0, recently introduced by Cresson. Some interesting consequences are obtained and discussed. Copyright (c) 2007 John Wiley & Sons, Ltd.