Abstract:
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.
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