## Abstract and Applied Analysis

### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 357821, 9 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.aaa/1395858292

Digital Object Identifier
doi:10.1155/2014/357821

Mathematical Reviews number (MathSciNet)
MR3166602

Zentralblatt MATH identifier
07022218

#### Citation

Mei, Zhan-Dong; Peng, Ji-Gen; Gao, Jing-Huai. Convoluted Fractional $C$ -Semigroups and Fractional Abstract Cauchy Problems. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 357821, 9 pages. doi:10.1155/2014/357821. https://projecteuclid.org/euclid.aaa/1395858292

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