Fractional Evolution Equations Governed by Coercive Differential Operators

This paper is concerned with evolution equations of fractional order D(alpha)u(t) = Au(t); u(0) = u(0),u'(0) = 0, where A is a differential operator corresponding to a coercive polynomial taking values in a sector of angle less than pi and 1 < alpha < 2. We show that such equations are well posed in the sense that there always exists an alpha-times resolvent family for the operator A. Copyright (C) 2009 Fu-Bo Li et al.