Báo cáo hoa học: " Research Article Vartiational Optimal-Control Problems with Delayed Arguments on Time Scales"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Vartiational Optimal-Control Problems with Delayed Arguments on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 84o386 15 pages doi 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 1 Department of Mathematics and Computer Science Cankaya University 06530 Ankara Turkey 2 Institute of Space Sciences . BOX MG-23 76900 Magurele-Bucharest Romania Correspondence should be addressed to Thabet Abdeljawad Maraaba thabet@ Received 11 August 2009 Revised 3 November 2009 Accepted 16 November 2009 Recommended by Paul Eloe 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. 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. 1. Introduction The calculus of variations interacts deeply with some branches of sciences and engineering for example geometry economics electrical engineering and so on 1 Optimal control problems appear in various disciplines of sciences and engineering as well 2 Time-scale calculus was initiated by Hilger see 3 and the references therein being in mind to unify two existing approaches of dynamic models difference and differential equations into a general framework This kind of calculus can be used to model dynamic processes whose time domains are more complex than the set of integers or real numbers 4 Several potential applications for this new theory were reported see . 4-6 and the references therein . Many researchers studied calculus of variations on time scales. Some of .

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