Uniqueness and existence of positive solutions forsingular fractional differential equations

Abstract

In this article, we study the existence of positive solutions for the singular fractional boundary value problem [GRAPHICS] where 1 < alpha <= 2, 0 < xi <= 1/2, a is an element of [0, infinity), 1 < alpha - delta < 2, 0 < beta(i) < 1, A, B-i, 1 <= i <= k, are real constant, D-alpha is the Reimann-Liouville fractional derivative of order alpha. By using the Banach's fixed point theorem and Leray-Schauder's alternative, the existence of positive solutions is obtained. At last, an example is given for illustration.