Complex powers of multivalued linear operators with polynomially bounded \(C\)-resolvent. (English) Zbl 07405374
Summary: 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 multivalued linear operator; \(C\)-resolvent set; abstract incomplete fractional differential inclusion; abstract incomplete differential inclusion of second order; locally convex spaceReferences:
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