Fractional evolution equations governed by coercive differential operators (Q1030625)

Summary: This paper is concerned with evolution equations of fractional order \(D^{\alpha}u(t)=Au(t)\); \(u(0)=u_{0}\), \(u^{\prime}(0)=0,\) 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 \(A\).