40,250 research outputs found
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
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