The Research For Two Classes Of Fractional Multi-point Boundary Value Problems

The research for fractional multi-point boundary value problems with a wide range of theoretical and practical significance, has been widespread concern, becomes the theoretical study of the nonlinear ordinary differential equation of an active and fruitful field of science. In this paper, the basic concept methods of material is selected, fixed point theorem and Leray-Schauder nonlinear alternative are used to solve the existence of solutions for two kinds of fractional multi-point boundary value problems.The first chapter, describes the research status of fractional differential equations and boundary value problems, we have a basic understanding of the fractional order ordinary differential equation boundary value problem, and introduces the main content of this paper.The second chapter, describes the theory of the Caputo fractional derivative,including definition, lemma and theorem, they are the useful tools by the means of nonlinear functional analysis. By the means of Banach fixed point theorem and Krasnoselskii fixed point theorem, similar to the classical analysis, the existence and uniqueness of solutions for fractional multi-point boundary value problems is researched under the premise of differential order number q ?(1, 2]. In addition,coefficients of boundary conditions are required, the results of the relevant literature is generalized in the end.The third chapter, describes the important lemma that will be used in the following, the existence of solutions for fractional multi-point boundary value problems is considered under the premise of differential order number q ?(1, 2]. Based on the new boundary conditions, extend and improve the conditions of the original literature, by the means of Banach fixed point theorem, Krasnoselskii fixed point theorem and Leray-Schauder nonlinear alternative, existence and uniqueness results for the solutions are established.The forth chapter, we take into account the deficiencies of this article and further research.