We study the duality theory for fractional resolvents, extending and improving some corresponding theorems on semigroups. As applications, we develop the variational technique to analyze the finite-approximate controllability of a backward fractional control system with a right-sided Riemann-Liouville fractional derivative. Moreover, validity of our theoretical findings is given by a fractional diffusion model.

中文翻译：

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分数分解剂的对偶理论及其在后向分数控制系统中的应用

我们研究分数分解的对偶理论，扩展和改进了半群上的一些相应定理。作为应用，我们开发了变分技术来分析带有右侧Riemann-Liouville分数阶导数的后向分数阶控制系统的有限逼近可控性。此外，我们的理论发现的有效性由分数扩散模型给出。