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Convoluted fractional \(C\)-semigroups and fractional abstract Cauchy problems. (English) Zbl 1472.47032

Summary: We present the notion of convoluted fractional \(C\)-semigroup, which is the generalization of convoluted \(C\)-semigroup in the Banach space setting. We present two equivalent functional equations associated with convoluted fractional \(C\)-semigroup. Moreover, the well-posedness of the corresponding fractional abstract Cauchy problems is studied.

MSC:

47D06 One-parameter semigroups and linear evolution equations
34G10 Linear differential equations in abstract spaces
34A08 Fractional ordinary differential equations
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