The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.Comment: Accepted (19 February 2010) for publication in Computers and Mathematics with Application

Backward variational approach on time scales with an action depending on the free endpoints

We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory of time scales via the backward nabla differential operator.Comment: Submitted 17-Oct-2010; revised 18-Dec-2010; accepted 4-Jan-2011; for publication in Zeitschrift fuer Naturforschung