| 摘要: |
| 研究了Hilbert空间中具有非局部条件的Sobolev型Hilfer分数阶发展方程的有限近似可控性.在控制系统对应的线性系统是近似可控的这一假设下，通过使用分数阶微积分理论、半群理论、变分法和Schaefer不动点定理，得到了控制系统有限近似可控的充分条件. |
| 关键词: Hilfer分数阶导数 发展方程 非局部条件 有限近似可控性 |
| DOI：10.3969/J.ISSN.1000-5137.2020.04.001 |
| 分类号:O231.2 |
| 基金项目:新疆维吾尔自治区自然科学基金项目（2019D01A71）；新疆维吾尔自治区高校科研计划项目（XJEDU2018Y033）；国家自然科学基金（11961069）；新疆优秀青年科技人才培训计划项目（2019Q022） |
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| Finite-approximate controllability of Hilfer fractional evolution equations of Sobolev type with nonlocal conditions |
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WANG Xingzhao, GU Haibo, MA Lina, CHEN Yiru
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School of Mathematics Sciences, Xinjiang Normal University, Urumqi 830017, Xinjiang, China
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| Abstract: |
| We discuss the finite-approximate controllability of Hilfer fractional evolution equations of Sobolev type with nonlocal conditions in Hilbert spaces.With the assumption that the corresponding linear system is approximately controllable,we obtain sufficient conditions for finite-approximate controllability of the control system by using fractional calculus, semigroup theory, variational analysis and Schaefer fixed point theorem. |
| Key words: Hilfer fractional derivative evolution equation nonlocal conditions finite-approximate controllability |
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