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Báo cáo hóa học: " Research Article Positive Solution of Singular Boundary Value Problem for a Nonlinear Fractional Differential Equation"

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 Positive Solution of Singular Boundary Value Problem for a Nonlinear Fractional Differential Equation | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 297026 12 pages doi 10.1155 2011 297026 Research Article Positive Solution of Singular Boundary Value Problem for a Nonlinear Fractional Differential Equation Changyou Wang 1 2 3 Ruifang Wang 2 4 Shu Wang 3 and Chunde Yang1 1 College of Mathematics and Physics Chongqing University of Posts and Telecommunications Chongqing 400065 China 2 Key Laboratory of Network Control Intelligent Instrument Chongqing University of Posts and Telecommunications Ministry of Education Chongqing 400065 China 3 College of Applied Sciences Beijing University of Technology Beijing 100124 China 4 Automation Institute Chongqing University of Posts and Telecommunications Chongqing 400065 China Correspondence should be addressed to Changyou Wang wangcy@cqupt.edu.cn Received 16 August 2010 Revised 16 November 2010 Accepted 9 January 2011 Academic Editor M. Salim Copyright 2011 Changyou Wang 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. The method of upper and lower solutions and the Schauder fixed point theorem are used to investigate the existence and uniqueness of a positive solution to a singular boundary value problem for a class of nonlinear fractional differential equations with non-monotone term. Moreover the existence of maximal and minimal solutions for the problem is also given. 1. Introduction Fractional differential equation can be extensively applied to various disciplines such as physics mechanics chemistry and engineering see 1-3 . Hence in recent years fractional differential equations have been of great interest and there have been many results on existence and uniqueness of the solution of boundary value problems for fractional differential equations see 4-7 . Especially in 8 the authors have studied the following type of .