YANG Xiao,BAI Junjie,GE Qi*.Existence of solutions for a class of boundary value problems with hybrid fractional q-differences[J].Journal of Yanbian University,2015,41(01):21-24,41.
一类混合分数阶q-差分边值问题解的存在性
- Title:
- Existence of solutions for a class of boundary value problems with hybrid fractional q-differences
- 分类号:
- O175.6
- 文献标志码:
- A
- 摘要:
- 研究了一类带有分数阶q-差分边值条件的混合分数阶q-差分方程解的存在性.首先分析了格林函数的性质,然后借助Lipschitz条件,在Banach代数中利用不动点定理研究了该方程解的存在性,最后通过实例验证了所得结论的合理性.
- Abstract:
- We study the existence of solutions for a class of the fractional q-differences hybrid equation with the fractional q-differences boundary conditions. Firstly, some characteristics of the Green function were analyzed. The second, we obtained sufficient conditions for the existence of positive solutions to this equation under Lipschitz condition using fixed point theorems in Banach algebra. The end, the main results were illustrated with the aid of examples.
参考文献/References:
[1] Ferreira R A C. Nontrivial solutions for fractional q-difference boundary value problems[J]. Theory of Differential Equations, 2010,70:1-10.
[2] Ferreira R A C. Positive solutions for a class of boundary value problems with fractional q-differences[J]. Computers and Mathematics with Applications, 2011,61(2):367-373.
[3] Ricardo Almeida, Natália Martins. Existence results for fractional q-difference equations of order α∈]2,3[ with three-point boundary conditions[J]. Communications in Nonlinear Science and Numerical Simulation, 2014,19(6):1675-1685.
[4] Zhao Yulin, Chen Haibo, Zhang Qiming. Existence results for fractional q-difference equations with nonlocal q-integral boundary conditions[J]. Advances in Difference Equations, 2013,2013:1-15.
[5] Zhao Yulin, Ye Guobing, Chen Haibo. Multiple positive solutions of a singular semipositione integral boundary value problem for fractional q-derivatives equation[J]. Abstract and Applied Analysis, 2013,2013:1-12.
[6] 孙明哲,韩筱爽.一类分数阶q-差分边值问题的正解[J].延边大学学报:自然科学版,2013,39(4):252-255.
[7] Bashir Ahmad, Sotiris K Ntouyas. Fractional q-difference hybrid equations and inclusions with Dirichlet boundary conditions[J]. Advances in Difference Equations, 2014,2014:1-14.
[8] Sun Shurong, Zhao Yige, Han Zhenlai. The existence of solutions for boundary value problems of fractional hybrid differential equations[J]. Communications in Nonlinear Science and Numerical Simulation, 2012,17(12):4961-4967.
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备注/Memo
收稿日期: 2014-11-16 *通信作者: 葛琦(1975—),女,副教授,研究方向为常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”科学技术研究项目(2015—2016)