The Existence Of Solutions Of Boundary Value Problems For Some Classes Of Fractional Differential Equations

Fractional di?erential equations have gained important applications in vari-ous science ?elds, the last ten years, the research of fractional di?erential equa-tions developed rapidly. Although boundary value problem of fractional ordinarydi?erential equations has many results, the research progress of boundary valueproblem of the fractional functional di?erential equations is very slow, the resultsare rather less.In this paper, we main discuss the existence and multiplicity of solutions fordi?erent boundary value problem of nonlinear fractional functional di?erentialequations. The main contents as follows:In chapter 1, First we introduce the development and situation of the frac-tional di?erential equations, Secondly introducing main work of this paper, Lastwe brie?y introduce some basic concepts and properties of fractional integral andfractional derivative, and including the basic knowledge and some ?xed pointtheorem.In chapter 2, we discussed the existence and uniqueness of solutions for two-point boundary value problem. First, we ?nd out green function with discussingits properties, and change the di?erential equation into the equivalent integralequation, on this basis, we can obtain the existence results of solutions by ?xedpoint theorem.In chapter 3, we consider the existence of solutions for multi-point boundaryvalue problem of fractional functional di?erential equations. First, we ask outgreen function and change di?erential equation into equivalent integral equation,on this basis, we can gain the existence results of solutions by Schauder's ?xedpoint theorem and Banach contracting mapping principle.In chapter 4, we study the existence and multiplicity of solutions for bound-ary value problems of fractional di?erential equations, and give some examplesto illustrate the correctness of theorems.