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 and Uniqueness of Positive and Nondecreasing Solutions for a Class of Singular Fractional Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 421310 10 pages doi 2009 421310 Research Article Existence and Uniqueness of Positive and Nondecreasing Solutions for a Class of Singular Fractional Boundary Value Problems J. Caballero Mena J. Harjani and K. Sadarangani Departamento de Matemdticas Universidad de Las Palmas de Gran Canaria Campus de Tafira Baja 35017 Las Palmas de Gran Canaria Spain Correspondence should be addressed to K. Sadarangani ksadaran@ Received 24 April 2009 Accepted 14 June 2009 Recommended by Juan Jose Nieto We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets. Copyright 2009 J. Caballero Mena 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 Many papers and books on fractional differential equations have appeared recently. Most of them are devoted to the solvability of the linear fractional equation in terms of a special function see . 1 2 and to problems of analyticity in the complex domain 3 . Moreover Delbosco and Rodino 4 considered the existence of a solution for the nonlinear fractional differential equation DỊỊ u f t u where 0 a 1 and f 0 ữ X R R 0 a to is a given continuous function in 0 a X R. They obtained results for solutions by using the Schauder fixed point theorem and the Banach contraction principle. Recently Zhang 5 considered the existence of positive solution for equation D0Ị u f t u where 0 a 1 and f 0 1 X 0 to 0 to is a given continuous function by using the sub- and supersolution methods. In this paper we discuss the existence and uniqueness of a positive and nondecreasing solution to .