Fractional Differential Equation Boundary Value Problem And The Scores Of Impulsive Differential Equations With The Existence Of Problems

Fractional differential equations have a wide range of applications in mathematics itself and many aspects of modern science and technology. For example, we can find numerous applications in viscoelasticity, electrochemistry, control, porous media, etc. So, fractional differential equation is enjoying more interest among scholars in recent years. They have drawn some fine conclusions of the theory and application research for fractional differential equations.In this paper, we mainly discuss boundary value problems to a class of fractional differential equations and the existence of the solution to fractional differential equations with impulse. This thesis consists of four chapters.In chapter 1, we will introduce the history and current research situation of the fractional integral and derivative theory. And we briefly describe the major work done in this paper.In chapter 2, we will show some preliminary results, including basic definitions and properties of fractional integral and derivative, a couple of fixed point theorems.Chapter 3 is the focus of this thesis. In this chapter, we devoted to existence for the solution of various classes of boundary value problems for fractional differential equations. Some examples are provided to illustrate the results presents.In this chapter4, we concern with initial problems of a class of fractional differential equations with impulse. We get the sufficient condition that ensures the existence and uniqueness of the solution.