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Title: The stability and stabilization of infinite dimensional Caputo-time fractional differential linear systems
Author: Zitane, Hanaa
Boutoulout, Ali
Torres, Delfim F. M.
Keywords: Fractional differential equations
Fractional diffusion systems
Caputo derivative
Stability and stabilization in Hilbert spaces
Decomposition method
Issue Date: Mar-2020
Publisher: MDPI
Abstract: We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provide sufficient and necessary conditions for the exponential stability of the considered class of systems. Then, by assuming that the system dynamics is symmetric and uniformly elliptic and by using the properties of the Mittag-Leffler function, we provide sufficient conditions that ensure strong stability. Finally, we characterize an explicit feedback control that guarantees the strong stabilization of a controlled Caputo time fractional linear system through a decomposition approach. Some examples are presented that illustrate the effectiveness of our results.
Peer review: yes
DOI: 10.3390/math8030353
Appears in Collections:CIDMA - Artigos
DMat - Artigos
SCG - Artigos

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