一类具参数的分数阶差分方程边值问题解的存在唯一性  

Existence and Uniqueness of Solutions of Boundary Value Problems for Fractional Order Difference Equations with a Parameter

作　　者：肖涵[1] 吴正[1] 王良龙[1] 

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《合肥学院学报（综合版）》2016年第4期5-10,共6页Journal of Hefei University：Comprehensive ED

基　　金：国家自然科学基金(11401002;11301004);安徽省自然科学基金(1508085QA01);安徽省高校自然科学重点研究项目(KJ2014A010);安徽省高等教育质量工程项目(2015jyxm057);安徽大学质量提升计划项目(ZLTS2015052)资助

摘　　要：研究了阶数介于3到4之间的一类分数阶差分方程的边值问题。通过构造相应的Green函数,证明Green函数的正性性质,利用Banach压缩映像原理和Brouwer不动点定理,在合适的条件下,获得了边值问题解的存在唯一性。特别地,当阶数v=4时,原问题变为整数阶差分方程边值问题,研究结果表明,分数阶差分方程边值问题与整数阶差分方程边值问题具有本质区别。This paper is concerned with boundary value problems of fractional difference equations with the order between 3 to 4. Green function is technically constructed, the positivity of Green function is obtained. Under the suitable conditions, the existence and uniqueness of solutions of boundary value problems for fractional order difference equations with a parameter is proved by using of Banach contraction mapping principle and Brouwer fixed point theorem. In particular, the difference between fractional order difference equations and integer order difference equations is found, which is significant on research of fractional order difference equations.

关 键 词：分数阶差分方程 GREEN函数 BROUWER不动点定理 压缩映象原理 

分 类 号：O241.84[理学—计算数学]