ZHU Xiangyu,SUN Mingzhe.Existence of positive solution for a class of fractional difference equations[J].Journal of Yanbian University,2014,40(01):25-30.
一类分数阶差分方程正解的存在性
- Title:
- Existence of positive solution for a class of fractional difference equations
- Keywords:
- fractional-order difference equations; boundary value problem; Green’s function; existence of solutions
- 分类号:
- O175.6
- 文献标志码:
- A
- 摘要:
- 研究了一类有限非线性分数阶差分方程边值问题正解的存在性.首先利用分数阶差分方程及其边值条件给出了Green函数,并分析了其性质; 然后利用Krasnosel’skii不动点定理,建立了这类分数阶差分方程边值问题正解的存在性定理.
- Abstract:
- We studied the existence of positive solutions of the boundary value problem for a nonlinear finite fractional difference equation. First, according to fractional difference equation and its boundary conditions, we constructed the Green’s function and analyzed its properties. Then, by using the Krasnosel’skii fixed point theorem we obtained sufficient conditions for the existence of positive solutions of the boundary value problem for the nonlinear finite difference equation.
参考文献/References:
[1] Miller K S, Ross B. Fractional difference calculus[C]//Procedings of the internations symposium on univalent functions. Koriyama: Fractional Calculus and Their Applications Nihon University, 1988:139-152.
[2] Atici F M, Eloe P W. A transform method in discrete fractional calculus[J]. Int J Difference Equ, 2007,2(2):165-176.
[3] Atici F M, Eloe P W. Initial value problems in discrete fractional calculus[J]. Proc Amer Math Soc, 2009,137:981-989.
[4] Goodrich C S. Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions[J]. J Comput Math Appl, 2011,61(21):191-202.
[5] Atici F M, Eloe P W. Two-point boundary value problems for finite fractional difference equations[J]. J Difference Equ Appl, 2011,17(4):445-456.
[6] Zhao Yige, Sun Shurong,Han Zhenlai. The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations[J]. J Commun Nonlinear Sci Number Simulat, 2011(16):2086-2097.
[7] 时宝,张德存,盖久明.微分方程理论及其应用[M].北京:国防工业出版社,2005:13.
[8] 程金发.分数阶差分方程理论[M].厦门:厦门大学出版社,2010.
[9] Chen F Q. Extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces[J]. Acta Math Appl Sinica, 2001,17:289-298.
相似文献/References:
[1]慎闯,金光植.一类带有分数阶分离边值条件的分数阶差分方程[J].延边大学学报(自然科学版),2012,38(04):265.
[2]孙明哲,侯成敏.一类分数阶q-差分系统边值问题解的存在性[J].延边大学学报(自然科学版),2015,41(01):10.
SUN Mingzhe,HOU Chengmin.Existence of solutions for boundary value problems with a coupled system of fractional q -differences[J].Journal of Yanbian University,2015,41(01):10.
[3]吴双,慎闯,侯成敏*.一类分数阶泛函差分边值问题解的存在性[J].延边大学学报(自然科学版),2014,40(01):11.
WU Shuang,SHEN Chuang,HOU Chengmin*.The existence of solution for a class of fractional functional difference boundary value problem[J].Journal of Yanbian University,2014,40(01):11.
[4]孙明哲,侯成敏.一类带有参数的q -差分方程边值问题正解的存在性[J].延边大学学报(自然科学版),2015,41(02):124.
SUN Mingzhe,HOU Chengmin.Existence of positive solutions of q -differences equations with parameter[J].Journal of Yanbian University,2015,41(01):124.
[5]徐佳宁,龚学,吴凡,等.一类二阶q-对称差分方程两点边值问题解的存在性[J].延边大学学报(自然科学版),2015,41(03):189.
XU Jianing,GONG Xue,WU Fan,et al.Existence of solutions for a class of q -symmetric difference equation two points boundary value problem[J].Journal of Yanbian University,2015,41(01):189.
[6]金小桢,侯成敏*.一类非线性分数阶q -对称差分方程边值问题正解的存在性[J].延边大学学报(自然科学版),2017,43(01):1.
JIN Xiaozhen,HOU Chengmin*.Existence of positive solutions for boundary value problems of a class of nonlinear fractional q -symmetry differences equation[J].Journal of Yanbian University,2017,43(01):1.
[7]董强,侯成敏*.具有p -Laplacian算子的delta-nabla分数阶
差分边值问题正解的存在性[J].延边大学学报(自然科学版),2019,45(04):283.
DONG Qiang,HOU Chengmin*.Existence of positive solutions for p -Laplacian fractional differenceinvolving the discrete delta-nabla fractional boundary value problem[J].Journal of Yanbian University,2019,45(01):283.
[8]于鹏艳,侯成敏*.一类分数阶微分包含耦合系统边值问题解的存在性[J].延边大学学报(自然科学版),2021,47(01):1.
YU Pengyan,HOU Chengmin*.The existence of solutions for a class of coupled systems of fractional differential inclusions with coupled boundary value problems[J].Journal of Yanbian University,2021,47(01):1.
[9]于洋,葛琦.一类Caputo型分数阶微分方程边值问题多重正解存在的充分条件[J].延边大学学报(自然科学版),2023,(02):95.
YU Yang,GE Qi.Sufficient conditions for the existence of multiple positive solutions for a Caputo type fractional-order differential equation boundary value problems[J].Journal of Yanbian University,2023,(01):95.
[10]葛月英,葛琦.一类Hadamard型分数阶微分方程边值问题的Lyapunov不等式及其解的存在性[J].延边大学学报(自然科学版),2023,(03):189.
GE Yueying,GE Qi.Existence of Lyapunov inequality and its solutions for a class of boundary value problems for fractional differential equations of Hardmard type[J].Journal of Yanbian University,2023,(01):189.
备注/Memo
收稿日期: 2013-09-18 基金项目: 延边大学科研基金资助项目(601010027)作者简介: 祝相宇(1978—),女,讲师,研究方向为微分方程理论.