Study On The Existence And Multiplicity Of Solutions For Nonlinear Fractional Differential Equations

In this paper,we investigate three kinds of nonlinear fractional differential equations including Riemann-Liouville type and Caputo type.By using Leggett-Williams fixed point theorem,Schaefer fixed point theorem and fixed point exponent theory,we study the existence and multiplicity of solutions.The existing results of related literatures are generalized and improved.The structure of the text is as followsThe first chapter is the introduction,which gives the background and significance of the research,describes the current research situation of fractional differential equations at home and abroad,and lists the main results obtained in this paperIn chapter 2,for a class of Riemann-Liouville type fractional differential equations with fractional derivative boundary conditions,the existence and multiplicity of solutions for two-point boundary value problems are investigated by using Leggett-Williams fixed point theo-rem.An example is givenIn chapter 3,we study the multipoint boundary value problem for a class of fractional differential equations with fractional derivative boundary conditions.By using the fixed point exponent theory,we obtain the existence and multiplicity of solutions,and give some examplesIn chapter 4,we study the two-point boundary value problem for a class of fractional differential equations with impulsive terms.By using Schaefer fixed point theorem,we study the existence of solutions of the equation,and obtain the existence and unique solution of the equation by using the contraction mapping principle.Some sufficient conditions are given and corresponding examples are given.