分数阶微分方程组边值问题解的存在性  

Existence of Solutions For Boundary Value Problem of Fractional Differential Equation System

作　　者：高芳[1] 江卫华[2] 

机构地区：[1]衡水学院分院数理系,河北衡水053000 [2]河北科技大学理学院,河北石家庄050018

出　　处：《数学的实践与认识》2013年第10期254-260,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11171088);河北省自然科学基金(A2013208108)

摘　　要：研究分数阶微分方程组边值问题在一类新型的边界条件——分数阶分离边界条件下解的存在性.通过将微分方程组边值问题转化为与之等价的积分方程组,利用Banach不动点定理和Leray-Schauder非线性更替得到边值问题解存在的充分条件,并给出两个例子说明了主要结论.In this paper, we investigate the existence of solutions for boundary value problem of fractional differential equation system with fractional separation boundary conditions. With the aid of the equivalent integral equation system, Banach fixed point theorems and Leray- Schauder nonlinear alternative, we get some sufficient conditions for the existence of solutions .We also give two examples to illustrate the applicability of our results.

关 键 词：微分方程组 分数阶微分 分数阶积分 边值问题 不动点 

分 类 号：O175.8[理学—数学]