title: Semigroups of Linear Operators and Applications to Partial Differential Equations (Applied Mathematical Sciences)
author: Amnon Pazy
description: From the reviews: "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C0 semigroups." #Bulletin Applied Mathematical Sciences 4/85#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert." #Bulletin of the London Mathematical Society#2
zlib_text: mathematics
  Article
  The Stability and Stabilization of Inﬁnite
  Dimensional Caputo-Time Fractional Differential
  Linear Systems
  Hanaa Zitane 1,†
  , Ali Boutoulout 1,†
  and Delﬁm F. M. Torres 2,*,†
  1
  MACS Laboratory, Department of Mathematics, Faculty of Sciences, University of Moulay Ismail,
  11201 Meknes, Morocco; h.zitane@edu.umi.ac.ma (H.Z.); a.boutoulout@fs-umi.ac.ma (A.B.)
  2
  Center for Research and Development in Mathematics and Applications (CIDMA),
  Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
  *
  Correspondence: delﬁm@ua.pt; Tel.: +351-234-370-668
  †
  The authors contributed equally to this work.
  Received: 31 December 2019; Accepted: 2 March 2020; Published: 5 March 2020
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  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 pro