Abstract and Applied Analysis
Volume 2009 (2009), Article ID 438690, 14 pages
doi:10.1155/2009/438690
Research Article

Fractional Evolution Equations Governed by Coercive Differential Operators

Fu-Bo Li,1 Miao Li,1 and Quan Zheng2

1Department of Mathematics, Sichuan University, Chengdu 610064, China
2Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 24 November 2008; Revised 8 February 2009; Accepted 24 March 2009

Academic Editor: Paul Eloe

Copyright © 2009 Fu-Bo Li 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

This paper is concerned with evolution equations of fractional order Dαu(t)=Au(t); u(0)=u0, u′(0)=0, where A is a differential operator corresponding to a coercive polynomial taking values in a sector of angle less than π and 1<α<2. We show that such equations are well posed in the sense that there always exists an α-times resolvent family for the operator A.