Monotone Iterative Method for Two Types of Integral Boundary Value Problems of a Nonlinear Fractional Differential System with Deviating Arguments

Abstract

This paper concerns on two types of integral boundary value problems of a nonlinear fractional differential system, $i.e$ ., nonlocal strip integral boundary value problems and coupled integral boundary value problems. With the aid of the monotone iterative method combined with the upper and lower solutions, the existence of extremal system of solutions for the above two types of differential systems is investigated. In addition, a new comparison theorem for fractional differential system is also established, which is crucial for the proof of the main theorem of this paper. At the end, an example explaining how our studies can be used is also given.