The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems

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 provid...

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Bibliographic Details
Published in:	Mathematics (Basel) Vol. 8; no. 3; p. 353
Main Authors:	Zitane, Hanaa, Boutoulout, Ali, Torres, Delfim F. M.
Format:	Journal Article
Language:	English
Published:	MDPI AG 01.03.2020
Subjects:	caputo derivative decomposition method fractional differential equations fractional diffusion systems stability and stabilization in hilbert spaces
ISSN:	2227-7390, 2227-7390
Online Access:	Get full text
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Summary:	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 are symmetric and uniformly elliptical 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.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math8030353