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 Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 475126 17 pages doi 2011 475126 Research Article Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System Zigen Ouyang 1 Yuming Chen 2 and Shuliang Zou3 1 School of Mathematics and Physics School of Nuclear Science and Technology University of South China Hengyang 421001 China 2 Department of Mathematics Wilfrid Laurier University Waterloo Ontario Canada N2L 3C5 3 School of Nuclear Science and Technology University of South China Hengyang 421001 China Correspondence should be addressed to Zigen Ouyang zigenouyang@ Received 14 November 2010 Accepted 24 February 2011 Academic Editor Gary Lieberman Copyright 2011 Zigen Ouyang 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. Though boundary value problems for fractional differential equations have been extensively studied most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand delay is natural in practical systems. However not much has been done for fractional differential equations with delays. Therefore in this paper we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility. 1. Introduction In the past decades fractional differential equations have been intensively studied. This is due to the rapid development of the theory of fractional differential equations itself and the applications of such construction in various sciences .
