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)》 ›› 2024, Vol. 59 ›› Issue (4): 45-52.doi: 10.6040/j.issn.1671-9352.0.2023.005

•   • 上一篇    下一篇

分数阶耦合系统循环周期边值问题解的存在性

张伟(),付欣雨,倪晋波   

  1. 安徽理工大学数学与大数据学院, 安徽 淮南 232001
  • 收稿日期:2023-01-09 出版日期:2024-04-20 发布日期:2024-04-12
  • 作者简介:张伟(1990—), 男, 讲师, 博士, 研究方向为常微分方程定性理论. E-mail: zhangwei_azyw@163.com
  • 基金资助:
    安徽省自然科学基金资助项目(2208085QA05);安徽理工大学研究生创新基金项目(2023cx2146)

Existence results for a coupled system of fractional differential equations with cyclic periodic boundary conditions

Wei ZHANG(),Xinyu FU,Jinbo NI   

  1. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, Anhui, China
  • Received:2023-01-09 Online:2024-04-20 Published:2024-04-12

RichHTML

7

PDF (PC)

547

摘要：

研究一类新的分数阶耦合系统共振边值问题, 考虑循环周期边值条件情形。此时不仅方程是耦合的, 边值条件也相互依赖。利用Mawhin连续性定理, 得到解的存在性准则, 并举例说明主要结论。

关键词: 分数阶耦合系统, 共振边值问题, 循环周期边值条件, Mawhin连续性定理

Abstract:

A new class of coupled fractional systems with resonance boundary value problems is studied, considering the case of cyclic periodic boundary conditions. In this case, not only are the equations coupled, but the boundary conditions are also interdependent. By using Mawhin's continuation theorem, the existence criteria for solutions are obtained and the main results are illustrated by an example.

Key words: fractional coupled system, resonance boundary value problem, cyclic periodic boundary condition, Mawhin's continuation theorem

中图分类号: 

  • O175.8
1 ROSS B . The development of fractional calculus 1695-1900[J]. Historia Math, 1977, 4, 75- 89.
doi: 10.1016/0315-0860(77)90039-8
2 宋晓娜. 分数阶混沌系统的控制与同步[M]. 北京: 科学出版社, 2018.
SONG Xiaona . Control and synchronization of fractional order chaotic systems[M]. Beijing: Science Press, 2018.
3 KILBAS A A , SRIVASTAVA H M , TRUJILLO J J . Theory and applications of fractional differential equations[M]. Amsterdam: Elsevier, 2006.
4 BAI Zhanbing , SUN Sujing , DU Zengji , et al. The green function for a class of Caputo fractional differential equations with a convection term[J]. Fractional Calculus and Applied Analysis, 2020, 23 (3): 787- 798.
doi: 10.1515/fca-2020-0039
5 SUN Bingzhi , JIANG Weihua , ZHANG Shuqin . Solvability of fractional differential equations with p-Laplacian and functional boundary value conditions at resonance[J]. Mediterranean Journal of Mathematics, 2022, 19 (1): 1- 18.
doi: 10.1007/s00009-021-01753-1
6 ZHANG Xingqiu , SHAO Zhuyan , ZHONG Qiuyan . Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable[J]. Fractional Calculus and Applied Analysis, 2022, 25 (4): 1507- 1526.
doi: 10.1007/s13540-022-00073-9
7 AHMAD B , ALSAEDI A , NTOUYAS S K , et al. Hadamard-type fractional differential equations, inclusions and inequalities[M]. Switzerland: Springer, 2017.
8 WANG J , ZADA A , WAHEED H . Stability analysis of a coupled system of nonlinear implicit fractional anti-periodic boundary value problem[J]. Mathematical Methods in the Applied Sciences, 2019, 42 (18): 6706- 6732.
doi: 10.1002/mma.5773
9 ZHANG Wei , NI Jinbo . Solvability for a coupled system of perturbed implicit fractional differential equations with periodic and anti-periodic boundary conditions[J]. Journal of Applied Analysis and Computation, 2021, 11 (6): 2876- 2894.
10 ZHANG Wei , LIU Wenbin , XUE Tingting . Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions[J]. Advances in Difference Equations, 2018, 2018, 1- 28.
doi: 10.1186/s13662-017-1452-3
11 AHMAD B , ALBLEWI M , NTOUYAS S K , et al. Existence results for a coupled system of nonlinear multi-term fractional differential equations with anti-periodic type coupled nonlocal boundary conditions[J]. Mathematical Methods in the Applied Sciences, 2021, 44 (11): 8739- 8758.
doi: 10.1002/mma.7301
12 AHMAD B , NIETO J J , ALSAEDI A , et al. A coupled system of Caputo-type sequential fractional differential equations with coupled (periodic/anti-periodic type) boundary conditions[J]. Mediterranean Journal of Mathematics, 2017, 14 (6): 1- 15.
13 HU Zhigang , LIU Wenbin . Solvability of a coupled system of fractional differential equations with periodic boundary conditions at resonance[J]. Ukrainian Mathematical Journal, 2014, 65 (11): 1619- 1633.
doi: 10.1007/s11253-014-0884-0
14 AHMAD B , ALMALKI A , NTOUYAS S K , et al. Existence results for a self-adjoint coupled system of three nonlinear ordinary differential equations with cyclic boundary conditions[J]. Qualitative Theory of Dynamical Systems, 2022, 21 (3): 1- 21.
15 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, 2005.
GUO Dajun , SUN Jingxian , LIU Zhaoli . Functional methods for nonlinear ordinary differential equation[M]. Jinan: Shandong Science and Technology Press, 2005.
[1] 杜睿娟. 一类半直线上三阶多点边值问题在dim Ker L=3共振情形下解的存在性[J]. 《山东大学学报(理学版)》, 2024, 59(4): 38-44.
[2] 倪云,刘锡平. 适型分数阶耦合系统正解的存在性和Ulam稳定性[J]. 《山东大学学报(理学版)》, 2023, 58(8): 82-91.
[3] 康聪聪. 一类二阶周期边值问题正解的存在性与多解性[J]. 《山东大学学报(理学版)》, 2023, 58(6): 68-76.
[4] 李春平,桑彦彬. 具有变号权函数的分数阶p-q-Laplacian方程组的多重解[J]. 《山东大学学报(理学版)》, 2022, 57(8): 95-102.
[5] 苏肖肖, 张亚莉. 带阻尼项的二阶差分方程周期边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2021, 56(2): 56-63.
[6] 武若飞. 奇异四阶m-点边值问题解的存在性[J]. 《山东大学学报(理学版)》, 2021, 56(2): 75-83.
[7] 刘梦雪, 李杰梅, 姚燕燕. 带有非线性边界条件的四阶边值问题的多解性[J]. 《山东大学学报(理学版)》, 2021, 56(2): 84-91.
[8] 孙妍妍,刘衍胜. 抽象空间中Hadamard分数阶微分方程奇异边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2020, 55(10): 95-103.
[9] 赵娇. 一类非线性三阶边值问题正解集的全局结构[J]. 《山东大学学报(理学版)》, 2020, 55(10): 104-110.
[10] 陈瑞鹏,李小亚. 带阻尼项的二阶奇异微分方程的正周期解[J]. 《山东大学学报(理学版)》, 2019, 54(8): 33-41.
[11] 巩增泰,高寒. n维模糊数值函数的预不变凸性[J]. 山东大学学报（理学版）, 2018, 53(10): 72-81.
[12] 王素云,李永军. 带超越共振点非线性项的二阶常微分方程边值问题的可解性[J]. 山东大学学报（理学版）, 2018, 53(6): 53-56.
[13] 王娇. 一类非线性二阶常微分方程 Dirichlet问题正解的存在性[J]. 山东大学学报（理学版）, 2018, 53(6): 64-69.
[14] 叶芙梅. 带导数项共振问题的可解性[J]. 山东大学学报（理学版）, 2018, 53(2): 25-31.
[15] 张申贵. 四阶变指数椭圆方程Navier边值问题的多解性[J]. 山东大学学报（理学版）, 2018, 53(2): 32-37.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发