Monotone Iterative Method To Two Types Of Nonlinear Fractional Conformable Differential Equations

In this thesis,we concentrate on the application of monotone iterative method to two types of nonlinear fractional conformable differential equations.First,the existence of the extremal solutions and the unique solution for a class of nonlinear fractional conformable p-Laplacian boundary value problem is studied.Secondly,the existence of the extremal solutions of boundary value problem for a class of nonlinear fractional conformable Langevin equation is studied.The whole paper is divided into three chapters:In chapter 1,we provide an introduction which consists of the research background of this article and the preliminary knowledge that will be used.Finally,the main task of this article is given.In chapter 2,we investigate a class of nonlinear fractional conformable p-Laplacian bound-ary value problem with nonlocal integral boundary conditions.Firstly,we establish the compari-son principle in the sense of fractional conformable derivative.Secondly,by using the established comparison principle and the monotone iterative method combined with the upper and lower solutions,the existence conditions of the extremal solutions and the unique solution of the boundary value problem are obtained.Finally,an example is used to verify the main results of this chapter.In chapter 3,we study a class of nonlinear fractional conformable Langevin equation with non-separated integro-differential strip-multi-point boundary conditions.By using the monotone iterative method combined with the upper and lower solutions,we not only obtain the existence of the extremal solutions for the nonlinear fractional conformable Langevin equation,but also conclude two computable explicit monotone iterative sequences that converge to the extremal solutions.In order to obtain the existence of the extremal solutions of the boundary value problem,the corresponding comparison principle is also established in this chapter.