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 The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral Boundary Conditions | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 546038 14 pages doi 2011 546038 Research Article The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral Boundary Conditions Meiqiang Feng 1 Xiaofang Liu 1 and Hanying Feng2 1 School of Applied Science Beijing Information Science Technology University Beijing 100192 China 2 Department of Mathematics Shijiazhuang Mechanical Engineering College Shijiazhuang 050003 China Correspondence should be addressed to Meiqiang Feng meiqiangfeng@ Received 19 December 2010 Accepted 26 January 2011 Academic Editor J. J. Trujillo Copyright 2011 Meiqiang Feng 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 expression and properties of Green s function for a class of nonlinear fractional differential equations with integral boundary conditions are studied and employed to obtain some results on the existence of positive solutions by using fixed point theorem in cones. The proofs are based upon the reduction of problem considered to the equivalent Fredholm integral equation of second kind. The results significantly extend and improve many known results even for integer-order cases. 1. Introduction Fractional calculus is an area having a long history its infancy dates back to three hundred years the beginnings of classical calculus. It had attracted the interest of many old famous mathematicians such as L Hospital Leibniz Liouville Riemann Grunward Letnikov and so forth 1 2 . As the old mathematicians expected in recent several decades fractional differential equations have been found to be a powerful tool in more and more fields such as materials physics mechanics and engineering 1-5 . For the basic theory and recent development of the subject we refer the reader to a text
