A decreasing operator method for a fractional initial value problem on infinite interval

Abstract

This paper considers the uniqueness of positive solutions for a fractional initial value problem involving Caputo fractional derivative ), and p(t) and q(t) are continuous functions. By imposing some suitable conditions on f , p, and q, we obtain the uniqueness of positive solutions for the problem, and we construct an iterative scheme to approximate the unique solution. Our approach is based on a fixed point theorem of decreasing operators on cones. In addition, two simply examples are presented to illustrate our main result.