Advances in Difference Equations
Volume 2009 (2009), Article ID 840386, 15 pages
doi:10.1155/2009/840386
Research Article

Vartiational Optimal-Control Problems with Delayed Arguments on Time Scales

Thabet Abdeljawad (Maraaba),1 Fahd Jarad,1 and Dumitru Baleanu1,2

1Department of Mathematics and Computer Science, Çankaya University, 06530 Ankara, Turkey
2Institute of Space Sciences, P.O. BOX MG-23, 76900 Magurele-Bucharest, Romania

Received 11 August 2009; Revised 3 November 2009; Accepted 16 November 2009

Academic Editor: Paul Eloe

Copyright © 2009 Thabet Abdeljawad (Maraaba) et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with variational optimal-control problems on time scales in the presence of delay in the state variables. The problem is considered on a time scale unifying the discrete, the continuous, and the quantum cases. Two examples in the discrete and quantum cases are analyzed to illustrate our results.