Topological Characteristics of solution sets for fractional evolution equations and applications to control systems
Topological Characteristics of solution sets for fractional evolution equations and applications to control systems
复制标题
分数阶进化方程解集的拓扑特性及其在控制系统中的应用
DOI：
10.12775/tmna.2019.033
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发表时间：
2019
影响因子：
0.7
通讯作者：
Li Gang
中科院分区：
文献类型：
--
作者：
Zhu Shouguo;Fan Zhenbin;Li Gang
本文研究了一个具有加权时滞初始条件的抽象Riemann-Liouville分数阶演化模型。我们开发的预解式技术，推广的半群方法，制定一个适当的概念，温和的解决方案，这个抽象的系统，并提出了相应的解决方案集的拓扑特征在加权空间。此外，鉴于拓扑特征，我们分析了抽象系统的近似能控性没有Lipschitz假设。最后，我们利用我们的理论结果解决了一个无穷维分数阶时滞扩散控制系统和一个有限维分数阶常微分控制系统。
This paper explores an abstract Riemann-Liouville fractional evolution model with a weighted delay initial condition. We develop the resolvent technique, a generalization of semigroup method, to formulate an appropriate notion of mild solutions to this abstract system and present the topological characteristics of the corresponding solution set in a weighted space. Furthermore, in view of the topological characteristics, we analyze the approximate controllability of the abstract system without Lipschitz assumption. We end up addressing an infinite dimensional fractional delay diffusion control system and a finite dimensional fractional ordinary differential control system by utilizing our theoretical findings.