SU Wei,LIU Chang,LI Dan,et al.Existence of positive solutions for a class of the boundary value problems of fractional q-difference equations[J].Journal of Yanbian University,2015,41(02):103-110.
一类分数阶q -差分方程边值问题正解的存在性
- Title:
- Existence of positive solutions for a class of the boundary value problems of fractional q-difference equations
- Keywords:
- fractional q-differences; Bananch space; upper and lower solution method; existence of solutions
- 分类号:
- O175.6
- 文献标志码:
- A
- 摘要:
- 研究了一类分数阶q-差分方程多点边值问题,其中控制函数含有分数阶导数.首先通过变换将该问题转化为带有分数阶积分控制的边值问题,并分析了格林函数的一些性质; 其次利用Arzela-Ascoli不动点定理及上下解方法,证明了该方程正解的存在性; 最后通过实例验证了本文所得结论的正确性.
- Abstract:
- We study a class of the boundary value problems of fractional q-difference equations. Here, the fractional derivative is contained in control function. Firstly, we transform the problem into a boundary value problem with fractional integrals control and analyze some properties of the Green function. Secondly, the existence of the solutions of the equation are proved by using the Arzela-Ascoli fixed point theorem in Banach space and upper and lower solution method. Finally, we give a example to illustrate our results.
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备注/Memo
收稿日期: 2015-04-12 基金项目: 国家自然科学基金资助项目(11161049)*通信作者: 何延生(1962—),男,副教授,研究方向为微分方程理论及应用.