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

Towards a combined fractional mechanics and quantization

A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional derivatives. The obtained results provide tools to carry out the quantization of nonconservative problems through combined fractional canonical equations of Hamilton type.Comment: This is a preprint of a paper whose final and definite form will be published in: Fract. Calc. Appl. Anal., Vol. 15, No 3 (2012). Submitted 21-Feb-2012; revised 29-May-2012; accepted 03-June-201

Nonessential Functionals in Multiobjective Optimal Control Problems

We address the problem of obtaining well-defined criteria for multiobjective optimal control systems. Necessary and sufficient conditions for an optimal control functional to be nonessential are proved. The results provide effective tools for determining nonessential objectives in vector-valued optimal control problems.Comment: Presented at the 5th Junior European Meeting on Control & Information Technology (JEM'06), September 20-22, 2006, Tallinn, Estoni