| In this thesis, we use several fixed point theorems, discussed the existence and uniqueness of solution for several classes of nonlinear fractional differential equations, and constructed some examples used to demonstrate what we have come to the conclusion.This thesis consists of six chapters:In chapter 1, we present the background, the current situation and the future tendency of the research on fractional differential equations.In chapter 2, we introduce the preliminaries which will be used in this thesis, including some definitions, properties of fractional calculus and conclusions of function spaces, as well as some fixed point theorems which are helpful in our study.In chapter 3, we studied with Caputo type sequential fractional differential equations with non-local boundary value conditions of fractional differential equations, we got two differential results. The first result using the Altman fixed point theorem, obtained with nonlocal boundary value conditions for the existence of the fractional differential equations. The second results is derived from the compression mapping principle in Banach Space for the existence and uniqueness of impulsive fractional differential equation. Finally, we give some specific examples of the application.In chapter 4, by using Schaefer fixed point theorem, we get the existence results of boundary value problems for nonlinear Langevin equation involving two fractional orders.Further, we use contraction mapping principle in Banach Space to given the existence and uniqueness results. At the end of this chapter we give a simple example to illustrate.In chapter 5, we studied a class of non-instantaneous impulse of fractional differential equations. Under appropriate conditions, by using the Banach fixed point and Krasnoselskii's fixed point theorem, we get the existence of the solution. Moreover, we give an example to illustrate the results.In chapter 6, we give a conclusion of our present work and make a plan for further research. |
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