YANG Changfa,HOU Chengmin*.Existence and uniqueness of solutions for a class of Caputo type fractional q -difference system with functional boundary value conditions[J].Journal of Yanbian University,2018,44(02):103-108，178.
一类带有泛函边值条件的Caputo型分数阶q -差分系统解的存在性与唯一性
- Title:
- Existence and uniqueness of solutions for a class of Caputo type fractional q -difference system with functional boundary value conditions
- 分类号:
- O175.6
- 文献标志码:
- A
- 摘要:
- 研究一类带有泛函边值条件的分数阶q-差分系统解的存在性和唯一性.首先,根据该系统解的表达式构造了4个算子,并定义了一个新的算子,将证明该系统解的存在性转化为证明新算子是否具有不动点.然后,运用Krasnoselskii不动点定理和Perov’s不动点定理,在合适的假设条件下证明了该系统解的存在性与唯一性.
- Abstract:
- We study the existence and uniqueness of solutions for a class of fractional q -differences system with functional boundary value conditions. Firstly, according to the expression of the system solution, four operators are constructed and a new operator is defined. Then we prove that the existence of the solution of the system transforms to prove whether the new operator has fixed point. Using Krasnoselskii fixed point theorem and Perov’s fixed point theorem, the existence and uniqueness of the solution of the system are proved under suitable assumptions.
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备注/Memo
*通信作者: 侯成敏(1963—),女,教授,研究方向为微分方程理论及其应用.