您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (2): 66-72.doi: 10.6040/j.issn.1671-9352.0.2016.213

• • 上一篇    下一篇

分数阶脉冲微分方程三点边值问题解的存在性和唯一性

张莎,贾梅*,李燕,李晓晨   

  1. 上海理工大学理学院, 上海 200093
  • 收稿日期:2016-05-16 出版日期:2017-02-20 发布日期:2017-01-18
  • 通讯作者: 贾梅(1963— ), 女, 副教授, 研究方向为微分方程理论及应用. E-mail:jiamei-usst@163.com E-mail:935247750@qq.com
  • 作者简介:张莎(1991— ), 女, 硕士研究生, 研究方向为微分方程理论及应用. E-mail:935247750@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11171220);沪江基金资助项目(B14005)

Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations

ZHANG Sha, JIA Mei*, LI Yan, LI Xiao-chen   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2016-05-16 Online:2017-02-20 Published:2017-01-18

摘要: 研究了一类分数阶脉冲微分方程三点边值问题解的存在性和唯一性。 利用Schauder不动点定理及压缩映射原理,获得了该边值问题解的存在性和唯一性定理。

关键词: 三点边值问题, 分数阶脉冲微分方程, 不动点定理, 存在性与唯一性, Caputo导数

Abstract: The existence and uniqueness of solutions is investigated for a class of three point boundary value problems of fractional differential equations with impulsive. By using the Schauder fixed point theorem and contraction mapping principle, some theorems about the existence and uniqueness of solutions for the boundary value problem are obtained.

Key words: three-point boundary value problem, Caputo derivative, fixed point theorem, existence and uniqueness, impulsive fractional differential equations

中图分类号: 

  • O175.8
[1] 傅希林, 闫宝强, 刘衍胜. 脉冲微分系统引论[M]. 北京:科学出版社, 2005. FU Xilin, YAN Baoqiang, LIU Yansheng. The introduction of impulsive differential systems[M]. Beijing: Science Press, 2005.
[2] 孙继涛, 张瑜, 赵寿为. 脉冲系统的分析与控制[M]. 北京:科学出版社, 2013. SUN Jitao, ZHANG Yu, ZHAO Shouwei. Analysis and control of pulse system[M]. Beijing: Science Press, 2013.
[3] 白占兵. 分数阶微分方程边值问题理论及应用[M]. 北京:中国科学技术出版社, 2012. BAI Zhanbing. Theory and applications of fractional differential equations boundary value problems[M]. Beijing: Science and Technology Press, 2012.
[4] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Amsterdam: Elsevier, 2006.
[5] DIETHELM K. The analysis of fractional differential equation[M]. Berlin Heidelberg: Springer-Verlag, 2010.
[6] 郭大钧, 孙经先, 刘兆理. 非线性常微分方程泛函方法[M]. 济南:山东科学技术出版社, 2006. GUO Dajun, SUN Jingxian, LIU Zhaoli. Functional methods for nonlinear ordinary differential equations[M]. Jinan: Shandong Science and Technology Press, 2006.
[7] AHMAD B, SIVASUNDARAM S. Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations[J]. Nonlinear Analysis Hybrid Systems, 2009, 3(3):251-258.
[8] 窦丽霞, 刘锡平, 金京福, 等. 分数阶积分微分方程多点边值问题解的存在性和唯一性[J]. 上海理工大学学报, 2012, 34(1):51-55. DOU Lixia, LIU Xiping, JIN Jingfu, et al. Existence and uniqueness of solutions of multi-point boundary value problems for integro-differential equations of fractional order[J]. Journal of University of Shanghai for Science and Technology, 2012, 34(1):51-55.
[9] WANG Jinrong, ZHOU Yong, MICHAL Feckan. On recent developments in the theory of boundary value problems for impulsive fractional differential equations[J]. Computers and Mathematics with Applications, 2012, 64(10):3008-3020.
[10] LIU Xiping, JIA Mei. Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations[J]. Mathematical Methods in the Applied Sciences, 2015, 39(3):475-487.
[11] ZHOU Jie, FENG Meiqiang. Greens function for sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application[J]. Boundary Value Problems, 2014, 2014(1):1-21.
[12] TIAN Yuansheng, BAI Zhanbing. Existence results for the three-point impulsive boundary value problem involving fractional differential equations[J]. Computers and Mathematics with Applications, 2010, 59(8):2601-2609.
[13] LI Xiaoping, CHEN Fulai, LI Xuezhu. Generalized anti-periodic boundary value problems of impulsive fractional differential equations[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(1):28-41.
[14] 陈强, 贾梅, 张海斌. 一类非线性分数阶微分方程四点边值问题解的存在性和唯一性[J]. 山东大学学报(理学版), 2015, 50(4):42-49. CHEN Qiang, JIA Mei, ZHANG Haibin. Existence and uniqueness of solutions for nonlinear fractional four-point boundary value problems[J]. Journal of Shandong University(Natural Science), 2015, 50(4):42-49.
[15] 杨浩, 刘锡平, 吴贵云. 一类分数阶p-Laplace算子微分方程非局部边值问题解的存在性[J]. 山东大学学报(理学版), 2015, 50(4):57-62. YANG Hao, LIU Xiping, WU Guiyun. Existence of the solutions for a type of nonlocal boundary value problems for fractional differential equations with p-Laplacian operator[J]. Journal of Shandong University(Natural Science), 2015, 50(4):57-62.
[16] 刘帅, 贾梅, 秦小娜. 带积分边值条件的分数阶微分方程解的存在性和唯一性[J]. 上海理工大学学报, 2014, 36(5):409-415. LIU Shuai, JIA Mei, QIN Xiaona. Existence and uniqueness of solutions of the fractional differential equation with integral boundary conditions[J]. Journal of University of Shanghai for Science and Technology, 2014, 36(5):409-415.
[17] YANG Liu, ZHANG Weiguo, LIU Xiping. A sufficient condition for the existence of a positive solution for a nonlinear fractional differential equation with the Riemann-Liouville derivative[J]. Applied Mathematics Letters, 2012, 25(25):1986-1992.
[1] 申柳肖,赵春. 基于尺度结构的竞争种群系统的最优输入率控制[J]. 山东大学学报(理学版), 2018, 53(7): 21-29.
[2] 曹雪靓,雒志学. 污染环境下森林发展系统的最优控制[J]. 山东大学学报(理学版), 2018, 53(7): 15-20.
[3] 李涛涛. 二阶半正椭圆微分方程径向正解的存在性[J]. 山东大学学报(理学版), 2017, 52(4): 48-55.
[4] 冯海星,翟成波. 高阶非线性分数阶微分方程系统的多个正解[J]. 山东大学学报(理学版), 2017, 52(12): 48-57.
[5] 荣文萍,崔静. 非Lipschitz条件下一类随机发展方程的μ-概几乎自守解[J]. 山东大学学报(理学版), 2017, 52(10): 64-71.
[6] 苏小凤,贾梅,李萌萌. 共振条件下分数阶微分方程积分边值问题解的存在性[J]. 山东大学学报(理学版), 2016, 51(8): 66-73.
[7] 陈彬. 格林函数变号的三阶周期边值问题[J]. 山东大学学报(理学版), 2016, 51(8): 79-83.
[8] 郭丽君. 非线性微分方程三阶三点边值问题正解的存在性[J]. 山东大学学报(理学版), 2016, 51(12): 47-53.
[9] 吴成明. 二阶奇异耦合系统正周期解的存在性[J]. 山东大学学报(理学版), 2015, 50(10): 81-88.
[10] 陈强, 贾梅, 张海斌. 一类非线性分数阶微分方程四点边值问题解的存在性和唯一性[J]. 山东大学学报(理学版), 2015, 50(04): 42-48.
[11] 杨浩, 刘锡平, 吴贵云. 一类分数阶p-Laplace算子微分方程非局部边值问题解的存在性[J]. 山东大学学报(理学版), 2015, 50(04): 56-62.
[12] 郑春华, 刘文斌. 一类具有时滞的分数阶微分方程边值问题正解的存在性[J]. 山东大学学报(理学版), 2015, 50(03): 73-79.
[13] 杨雪洁,孙国正*,陈雯. 一个拟线性奇摄动问题的激波解[J]. 山东大学学报(理学版), 2014, 49(04): 79-83.
[14] 周文学1,2, 刘海忠1. 一类分数阶微分方程边值问题解的存在性[J]. J4, 2013, 48(8): 45-49.
[15] 陈一鸣,孙慧,刘乐春,付小红. Legendre多项式求解变系数的分数阶Fredholm积分微分方程[J]. J4, 2013, 48(6): 80-86.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!