Fractional Evolution Equations Governed by Coercive Differential Operators

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