Geodesic
Complex powers of multivalued linear operators with polynomially bounded $C$-resolvent
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 363-385

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We construct complex powers of multivalued linear operators with polynomially bounded $C$-resolvent existing on an appropriate region of the complex plane containing the interval $(-\infty,0].$ In our approach, the operator $C$ is not necessarily injective. We clarify the basic properties of introduced powers and analyze the abstract incomplete fractional differential inclusions associated with the use of modified Liuoville right-sided derivatives. We also consider abstract incomplete differential inclusions of second order, working in the general setting of sequentially complete locally convex spaces.
Keywords: complex power of a multivalued linear operator, $C$-resolvent set, abstract incomplete fractional differential inclusion, abstract incomplete differential inclusion of second order, locally convex space. 
@article{CHFMJ_2020_5_3_a9,
     author = {M. Kosti\'c},
     title = {Complex powers of multivalued linear operators with polynomially bounded $C$-resolvent},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {363--385},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a9/}
}
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M. Kostić. Complex powers of multivalued linear operators with polynomially bounded $C$-resolvent. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 363-385. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a9/