New results on controllability of fractional evolution systems with order $ \alpha\in (1,2) $

By Yong Zhou, Jia Wei He. 2020

122 citations recorded by the source corpus.

This paper addresses some interesting results of mild solutions to fractional evolution systems with order \begin{document}$ \alpha\in (1,2) $\end{document} in Banach spaces as well as the controllability problem. Firstly, we deduce a new representation of solution operators and give a new concept of mild solutions for the objective equations by the Laplace transform and Mainardi's Wright-type function, and then we proceed to establish a new compact result of the solution operators when the sine family is compact. Secondly, the controllability results of mild solutions are obtained. Finally, an example is presented to illustrate the main results.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/811097a7a3454b1ab06ae17f48f6ba863c63ddc4

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In Applied Mathematics

In Control and Systems Engineering

In Modeling and Simulation

Citations in the corpus

Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2) (2019, methodology): “For further discussion in [18], the authors considered the controllability results for fractional evolution equations of order α ∈ (1, 2) by applying the concepts of Mainardi’s Wright function (a probability density function) and strongly continuous cosine families.”