Existence Of Solutions To Antiperiodic Boundary Value Problems For Fractional Differential Equations

Recently, the subject of fractional differential equations has received consid-erable attention as its important application in engineering, science and technol-ogy, economic.Boundary value problems to fractional differential equations is also an sig-nificant field, and an important methods to research this problem is fixed pointtheorem. Antiperiodic boundary value problems have practical application asthe same to periodic boundary value problems. In this thesis, we discuss theexistence of solutions to antiperiodic boundary value problems for fractional dif-ferential equations by means of fixed point theorems, and some new conclusionsare obtained.In chapter 1, we firstly introduce the applied background of research, mainresults and some preliminary results; In chapter 2, we discuss the existence of solu-tions to antiperiodic boundary value problems for fractional differential equationswith the use of Krasnosel'skill fixed point theorem; In chapter 3, we research theexistence of solutions to antiperiodic boundary value problems when the nonlin-ear term f is not independent of fractional derivative of unknown function x;In chapter 4, we discuss the antiperiodic boundary value problems for fractionaldifferential equations with impulses, and give some new theorems about existenceof solutions.