Abstract and Applied Analysis
Volume 2009 (2009), Article ID 438690, 14 pages
doi:10.1155/2009/438690
Fractional evolution equations governed by coercive differential operators
Fu-Bo Li1
, Miao Li1
and Quan Zheng3
1Department of Mathematics, Sichuan University, Chengdu 610064, China
3Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China
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.