一类分数阶微分方程边值问题解的存在性  

Existence of Solutions for the Fractional Differential Equations Boundary Value Problem

作　　者：任灿[1] 王刚[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008

出　　处：《四川理工学院学报（自然科学版）》2011年第3期288-291,共4页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：分数阶微分方程边值问题是从大量自然科学和工程技术问题中抽象出来的,在诸如流体力学、材料力学、天文学、经济学、生物学和医学等学科中有着广泛的应用,但目前关于分数阶微分方程多点边值问题的研究还不多见,文章研究了一类分数阶积分微分方程三点边值问题。在一定条件下,利用压缩映像原理及Krasnoselskii不动点定理,得到了分数阶微分方程积分边值问题解的存在性及唯一性。The boundary value Problem of fraetional differential equation is abstraeted fromt he problems of natural science and project technology,it is extensively applied in subject of hydromechanies,mechanics of materials,astronomy,economies,biology,medicine etc,but not so many papers discuss multi-point fractional order boundary value problems.Inspired by related works,in this paper,we discuss problems of three-point boundary value problem for fractional integro-differential equationsboundary value problem.By using the contraction mapping principle and Krasnoselskii fixed point theorem,existence and uniqueness of solutions for the fractional differential equations with integral boundary value problem are obtained.

关 键 词：分数阶 边值问题 不动点定理 存在性 

分 类 号：O175.8[理学—数学]