We present the notion of convoluted fractional -semigroup, which is the generalization of convoluted -semigroup in the Banach space setting. We present two equivalent functional equations associated with convoluted fractional -semigroup. Moreover, the well-posedness of the corresponding fractional abstract Cauchy problems is studied.
Zhan-Dong Mei. Ji-Gen Peng. Jing-Huai Gao. "Convoluted Fractional -Semigroups and Fractional Abstract Cauchy Problems." Abstr. Appl. Anal. 2014 (SI03) 1 - 9, 2014. https://doi.org/10.1155/2014/357821