FAN Chengtao,GE Qi*.Existence of solutions for a class of fractional q-differences equation with fractional boundary value conditions[J].Journal of Yanbian University,2015,41(03):207-214.
一类带有分数阶边值条件的分数阶q-差分方程解的存在性
- Title:
- Existence of solutions for a class of fractional q-differences equation with fractional boundary value conditions
- Keywords:
- fractional q-differences; complete metric space; fixed point theorem; existence and uniqueness of solutions
- 分类号:
- O175.6
- 文献标志码:
- A
- 摘要:
- 研究了一类带有分数阶q-差分边值条件的分数阶q-差分方程解的存在性和唯一性.首先分析了格林函数的一些性质; 其次分别利用完备度量空间上的不动点定理、Banach空间上的Schauder不动点定理和Banach压缩映像原理,证明了该方程解的存在性和唯一性; 最后通过实例验证了本文所得结论的正确性.
- Abstract:
- We study the existence and uniqueness of solutions for a class of the fractional q-differences equation with the fractional q-differences boundary conditions. Firstly, we analyze some properties of the Green function. Secondly, the existence and uniqueness of the solutions of the equation are proved by using the fixed point theorem in complete metric space, Schauder fixed point theorem in Banach space and Banach contraction principle. Finally, the correctness of the conclusion in this paper is verified by some examples.
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备注/Memo
收稿日期: 2015-01-12 *通信作者: 葛琦(1975—),女,副教授,研究方向为微分方程理论及其应用.基金项目: 国家自然科学基金资助项目(11161049); 吉林省教育厅“十二五”科技项目(012015042)