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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 357821, 9 pages
http://dx.doi.org/10.1155/2014/357821
Research Article

Convoluted Fractional -Semigroups and Fractional Abstract Cauchy Problems

1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2Institute of Wave and Information, School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Received 30 September 2013; Accepted 12 December 2013; Published 12 January 2014

Academic Editor: Juan J. Trujillo

Copyright © 2014 Zhan-Dong Mei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.