Riemann-Liouville 分数阶微分控制系统的逼近能控性

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 249-258.

Riemann-Liouville 分数阶微分控制系统的逼近能控性

施翠云¹(), 宾茂君²^,^*()

¹桂林理工大学南宁分校南宁 530001
²广西应用数学中心 (玉林师范学院) 广西玉林 537000

收稿日期:2025-02-19 修回日期:2025-07-19 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 宾茂君 E-mail:2899450273@qq.com;bmj1999@163.com
作者简介:施翠云,Email: 2899450273@qq.com
基金资助:
广西自然科学基金创新研究团队项目(2025GXNSFGA069001);广西自然科学基金(2022GXNSFFA035027);广西自然科学基金(2022GXNSFAA035617);广西高校中青年教师科研基础能力提升项目(2024KY0594);广西高校中青年教师科研基础能力提升项目(2023KY0599);广西高校中青年教师科研基础能力提升项目(2022KY0582)

Approximate Controllability of Riemann-Liouville Fractional Semilinear Evolution Systems

Cuiyun Shi¹(), Maojun Bin²^,^*()

¹Campus of Nanning, Guilin University of Technology, Nanning 530001
²Center for Applied Mathematics of Guangxi, Yulin Normal University, Guangxi Yulin 537000

Received:2025-02-19 Revised:2025-07-19 Online:2026-02-26 Published:2026-01-19
Contact: Maojun Bin E-mail:2899450273@qq.com;bmj1999@163.com
Supported by:
Natural Science Foundation Innovation Research Team Project of Guangxi(2025GXNSFGA069001);NSF of Guangxi(2022GXNSFFA035027);NSF of Guangxi(2022GXNSFAA035617);project of Guangxi Education Department(2024KY0594);project of Guangxi Education Department(2023KY0599);project of Guangxi Education Department(2022KY0582)

摘要/Abstract

摘要：

该文考虑 Banach 空间中 Riemann-Liouville 分数阶微分发展控制系统的逼近能控性. 首先, 证明 Riemann-Liouville 分数阶微分发展方程在 Banach 空间中存在 $C_{1-\alpha}$-温和解. 其次, 在合理的假设条件下证明 Riemann-Liouville 分数阶微分发展控制系统是逼近能控的. 最后给出一实际例子来验证该文的主要结果.

关键词: Riemann-Liouville 发展微分系统, $C_{1-\alpha}$-温和解, 存在性, 逼近能控

Abstract:

In this paper, We discuss Riemann-Liouville fractional evolution differential systems in Banach spaces. Firstly, the existence of $C_{1-\alpha}$-mild solutions for the Riemann-Liouville fractional evolution differential equations are established in Banach spaces. Secondly, we make some general assumptions to guarantee the approximate controllability of the associated Riemann-Liouville fractional evolution systems is also formulated and proved. In the end, an example is given to illustrate our main results.

Key words: Riemann-Liouville fractional evolution differential systems, $C_{1-\alpha}$-mild solutions, existence, approximate controllability

中图分类号:

O175.6

施翠云, 宾茂君. Riemann-Liouville 分数阶微分控制系统的逼近能控性[J]. 数学物理学报, 2026, 46(1): 249-258.

Cuiyun Shi, Maojun Bin. Approximate Controllability of Riemann-Liouville Fractional Semilinear Evolution Systems[J]. Acta mathematica scientia,Series A, 2026, 46(1): 249-258.

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