Boundary Value Problems For Fractional,Differencial Equations With Fractional Boundary Conditions

Fractional differencial equations has been developed rapidly in recent years.Especially,boundary value problems for fractional differencial equations with fractional boundary conditions make a great progress.This article studies the existence and uniqueness of solutions for boundary value problems for fractional differencial equations with fractional boundary conditions by using Schauder fixed point theorem and the contraction mapping principle. In chapter one, we introduce the development process of fractional ordinary differential equations, the research background and main results of this article.In chapter two, we introduce some preliminaries of boundary value problems for ordinary differential equations and theorem.In chapter three, we prove the existence and uniqueness of the solutions of the problem (1) and problem (2), In chapter four, we give some examples that illustrate our results.At last, in the summary section, we give the main frame of this article and the possible extended directions about this article in the future.