Convoluted Fractional C-Semigroups and Fractional Abstract Cauchy Problems

Abstract

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.