Existence Of Solutions For Initial Value Problems Of Some Kinds Of Fractional Differential Equations

In this paper, We mainly study the existence and uniqueness of solutions for the initial value problem of some kinds of fractional differential equation. Some sufficient conditions on existence and uniqueness are established, which enriched the theory for the solution of fractional differential equations. The main research work is divided into four chapters:In chapter one, We introduce the historical background and research status of the fractional calculus and fractional differential equations and the main work of this paper, And then give the related concepts and important lemma.In chapter two, We mainly discuss the existence and uniqueness of solutions for initial value problem of a type of the coupled system of fractional equations.In chapter three, We study the existence of positive solutions for a type of nonlinear fractional differential equations.In chapter four, We discuss the existence and uniqueness of solutions for sequential fractional functional differential equations.