Iterative positive solutions for singular nonlinear fractional differential equation with integral boundary conditions

Abstract

In this article, we study the existence of iterative positive solutions for a class of singular nonlinear fractional differential equations with Riemann-Stieltjes integral boundary conditions, where the nonlinear term may be singular both for time and space variables. By using the properties of the Green function and the fixed point theorem of mixed monotone operators in cones we obtain some results on the existence and uniqueness of positive solutions. We also construct successively some sequences for approximating the unique solution. Our results include the multipoint boundary problems and integral boundary problems as special cases, and we also extend and improve many known results including singular and non-singular cases.