The Existence Of Solutions For Several Kinds Of Fractional Differential Equations

Fractional differential equations have attracted the attention of many researchers in the last three decades because of their applications in numerous fields of science, en-gineering, physics, economy and so on. Unfortunately, the solutions that were obtained by applying analytic semigroup theory is inappropriate, because the Caputo fractional derivative does not satisfy the Leibniz product rule.The focus of this dissertation is to study the existence of mild solutions of impulsive fractional differential equations and the existence of solutions of1<a<2order fractional differential equations with nonlocal condition. In this dissertation, we mainly devote to the fixed point theory to research the existence of solutions of the given system. This dissertation is organized as follows:In the first chapter, we introduce the research background, our work and inno-vations, and systematically analyze development situations of fractional differential equations.Then, we briefly introduce basic knowledge of impulsive fractional differential equations and nonlocal fractional differential equations, and then give some definitions and theorems which are used in this dissertation.In the second chapter, we correct the inappropriate definition of mild solutions to impulsive fractional differential equation given by M.H.M.Rashid and give an ap-propriate definition of mild solutions. Then, as an application, we study the existence and uniqueness of mild solutions to the impulsive fractional differential equation by applying the contraction mapping principle.In the third chapter, by applying the fixed point theory, we study the existence of solutions of the1<α<2order fractional differential equations with nonlocal conditions.