New results for a class of boundary value problems involving impulsive fractional differential equations

Abstract

In this paper, a class of boundary value problems involving impulsive fractional differential equations is studied. By constructing Green's function, a natural formula of solutions is derived. By applying fixed point theorems for mixed monotone operator with perturbation and sum operator, some new results on the existence and uniqueness of positive solutions are obtained, and an iterative sequence is constructed to approximate the positive solutions.