Geodesic
Necessary and sufficient conditions for the approximate controllability of fractional linear systems via C−semigroups
Filomat, Tome 36 (2022) no. 5, p. 1451

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The approximate controllability of fractional linear evolution systems is considered in this paper. Firstly, the definitions of the mild solution and the approximate controllability of fractional linear evolution systems are obtained by using the theory of C−semigroups. Secondly, a new set of necessary and sufficient conditions are established to examine that linear system is approximately controllable with the help of symmetric operator. Moreover, the restricted condition of the state space is weakened by means of the dual mapping. Finally, as applications, the approximate controllability of nonlinear evolution systems are derived under the assumption that the corresponding linear system is approximately controllable. Our work essentially improves and generalized the corresponding results which are based on strongly continuous semigroups.
DOI : 10.2298/FIL2205451L
Classification : 47D60, 34K35, 34K37
Keywords: Fractional linear differential systems, Approximate controllability, C−semigroup, Duality mapping, Mild solution 
Tingting Lian; Zhenbin Fan; Gang Li. Necessary and sufficient conditions for the approximate controllability of fractional linear systems via C−semigroups. Filomat, Tome 36 (2022) no. 5, p. 1451 . doi: 10.2298/FIL2205451L
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     title = {Necessary and sufficient conditions for the approximate controllability of fractional linear systems via {C\ensuremath{-}semigroups}},
     journal = {Filomat},
     pages = {1451 },
     year = {2022},
     volume = {36},
     number = {5},
     doi = {10.2298/FIL2205451L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2205451L/}
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