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

Abstract

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 (α, β), α > 0, β >0, recently introduced by Cresson. Some interesting consequences are obtained and discussed. Copyright © 2007 John Wiley & Sons, Ltd.