Abstr. Appl. Anal. 2014 (SI03), 1-9, (2014) DOI: 10.1155/2014/357821
Zhan-Dong Mei, Ji-Gen Peng, Jing-Huai Gao
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.