Necessary and sufficient conditions for the approximate controllability of fractional linear systems via C−semigroups
Necessary and sufficient conditions for the approximate controllability of fractional linear systems via C−semigroups
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分数阶线性系统C半群近似可控性的充分必要条件
作者：
Tingting Lian;Zhenbin Fan;Gang Li
研究了分数阶线性发展系统的近似能控性。首先，利用C？半群其次，利用对称算子建立了一组新的充分必要条件，证明了线性系统是近似能控的。此外，通过对偶映射的方法，削弱了状态空间的约束条件。最后，作为应用，在相应的线性系统近似能控的假设下，得到了非线性发展系统的近似能控性。我们的工作实质上改进和推广了基于强连续半群的相应结果。
The approximate controllability of fractional linear evolution systems is considered in this paper. Firstly, the definitions of the mild solution and the approximate controllability of fractional linear evolution systems are obtained by using the theory of C?semigroups. Secondly, a new set of necessary and sufficient conditions are established to examine that linear system is approximately controllable with the help of symmetric operator. Moreover, the restricted condition of the state space is weakened by means of the dual mapping. Finally, as applications, the approximate controllability of nonlinear evolution systems are derived under the assumption that the corresponding linear system is approximately controllable. Our work essentially improves and generalized the corresponding results which are based on strongly continuous semigroups.
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