[1]范成涛,李怀义,葛琦*.一类有序分数阶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),2017,43(02):95-103.
　FAN Chengtao,LI Huaiyi,GE Qi*.Existence of solutions for boundary value problems with a coupled system of sequential fractional q -differences[J].Journal of Yanbian University,2017,43(02):95-103.
点击复制

一类有序分数阶q -差分系统边值问题解的存在性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第43卷 期数: 2017年02期 页码: 95-103 栏目: 基础科学研究 出版日期: 2017-07-20
Title:
Existence of solutions for boundary value problems with a coupled system of sequential fractional q -differences
作者:
范成涛1;  李怀义2;  葛琦1*
1.延边大学理学院 数学系, 吉林 延吉 133002; 2.延吉市第一高级中学 数学组, 吉林 延吉 133000
Author(s):
FAN Chengtao1;  LI Huaiyi2;  GE Qi1*
1.Department of Mathematics, College of Science, Yanbian University, Yanji 133002, China; 2.Math Team, Yianji First High School, Yanji 133000, China
关键词:
有序分数阶q-差分系统;  不动点定理;  解的存在性
Keywords:
sequential fractional q -differences system;  fixed point theorem;  existence of solutions
分类号:
O175.6
文献标志码:
A
摘要:
研究了一类有序分数阶q-差分系统解的唯一性和存在性.首先利用q-指数函数给出了该方程解的表达式,然后分别利用Leray-Schauder选择定理、Krasnoselskii不动点定理和Banach压缩映像原理证明了该系统解的存在性和唯一性.
Abstract:
We study the existence and uniqueness of solutions for a class of the sequential fractional q -differences system. Firstly, using q -exponential, a representation for the solution to this equation is given. Then the existence and uniqueness of solutions are proven by using Leray-Schauder alternative theorem, Krasnoselskii fixed point theorem and Banach contraction mapping principle.

参考文献/References:

[1] Jackson F H. On q-definite integrals, quart[J]. J Pure Appl Math, 1910,41:193-203.
[2] Al-Salam W A. Some fractionalq-integrals and q-derivatives[J]. Proc Edinb Math Soc, 1996,15(2):135-140.
[3] Agarwal R P. Certain fractional q-integrals and q-derivatives[J]. Proc Cambridge Philos Soc, 1996,66:365-370.
[4] Ernst T. q-Bernoulli and q-Euler polynomials, an umbral approach[J]. International Journal of Difference Equations, 2006,1(1):31-80.
[5] Ernst T. q-Pascal and q-Bernoulli matrices, an umbral approach[J]. Advances in Dynamical Systems and Applications, 2008,3(2):251-282.
[6] 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(48):1-15.
[7] Li Yanfeng, Yang Wengui. Monotone iterative method for nonlinear fractional q-difference equations with integral boundary conditions[J]. Advances in Difference Equations, 2015,2015(294):1-10.
[8] Suantai S, Ntouyas S K, Asawasamrit S, et al. A coupled system of fractional q-integro-difference equations with nonlocal fractional q-integral boundary conditions[J]. Advances in Difference Equations, 2015,2015(1):1-21.
[9] Ahmad B, Ntouyas S K, Tariboon J, et al. Impulsive fractional q-integro-difference equations with separated boundary conditions[J]. Applied Mathematics and Computation, 2016,281:199-213.
[10] Semary M S, Hassan H N. The homotopy analysis method for q-difference equations[J]. Ain Shams Engineering Journal, 2016,4:1-7.
[11] 葛琦,侯成敏.一类有序分数阶q-差分方程解的存在性[J].吉林大学学报(理学版),2015,53(3):377-382.

相似文献/References:

[1]杨潇,白俊杰,葛琦*.一类混合分数阶q-差分边值问题解的存在性[J].延边大学学报(自然科学版),2015,41(01):21.
　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(02):21.
[2]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(02):124.
[3]范成涛,葛琦.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[J].延边大学学报(自然科学版),2015,41(03):207.
　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(02):207.
[4]田野,张翼菲,葛琦*.一类混合二阶q-对称差分边值问题解的存在性[J].延边大学学报(自然科学版),2016,42(01):15.
　TIAN Ye,ZHANG Jifei,GE Qi*.Existence of solutions for a hybrid second-order q-symmetric difference boundary value problems[J].Journal of Yanbian University,2016,42(02):15.
[5]杨昌发,侯成敏*.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[J].延边大学学报(自然科学版),2018,44(02):103.
　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.
[6]黄明辉.变时滞非线性微分方程零解的渐近稳定性[J].延边大学学报(自然科学版),2019,45(01):1.
　HUANG Minghui.Asymptotic stability of the zero solution for nonlinear differentialequations with variable delays[J].Journal of Yanbian University,2019,45(02):1.
[7]甘亦苗,侯成敏*.一类Hadamard型分数阶微分方程解的存在唯一性[J].延边大学学报(自然科学版),2021,47(02):95.
　GAN Yimiao,HOU Chengmin*.The existence and uniqueness of the solutions of a class of Hadamard type fractional differential equations[J].Journal of Yanbian University,2021,47(02):95.
[8]李小龙.Banach空间中分数阶微分方程Robin边值问题解的存在性[J].延边大学学报(自然科学版),2022,(02):95.
　LI Xiaolong.Existence of solutions for Robin boundary value problems of fractional differential equation in Banach spaces[J].Journal of Yanbian University,2022,(02):95.
[9]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,(02):189.

备注/Memo

收稿日期: 2017-03-07 *通信作者: 葛琦(1975—),女,副教授,研究方向为微分方程理论及应用.
基金项目: 国家自然科学基金资助项目(11161049); 2015—2016年度吉林省教育厅“十二五”科技项目(吉教科合字[2015]第36号)

更新日期/Last Update: 2017-06-20