The Theoretical Research On Existence Of Solutions For Two Kinds Of Fractional Differential Equations

In this paper,firstly,we study the boundary value problems for a kind of fractional difference equations with Sturm-Liouville boundary conditions,and get the existences and multiplicity of solutions.Next,we study the eigenvalues problems for a kind of fractional linear differential equations,establish the relationship between eigenvalues and existence of solutions for nonlinear differential equations.According the research problems,the paper consists of five chapters:Chapter 1 is the introduction,which introduces the background,the history and the research status of fractional differential equations.Finally,the research contents are pointed out.Chapter 2 introduce the basic calculation formulas on fractional differential equations,basic definitions and theorems which would be used in article.In Chapter 3,we study the existence of solutions for a kind of boundary value problems of fractional differential equations with Sturm-Liouville boundary conditions.By using two-critical-point the-orems and three-critical-point theorems,we obtain the existence of two and three classical solutions for the boundary problem separately.In Chapter 4,the eigenvalues and eigenfunctions for a kind of fractional difference equations are studied by Laplace transformation and inverse Laplace transformation.Next,we use topological degree theory establish the relationship between the eigenvalue and solutions for nonlinear problem with same conditions.Chapter 5 summarizes the current work and the prospects the future work.