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The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.

&lt;i&gt;α&lt;/i&gt;-Times Integrated C Semigroups and Strong Solution of Abstract Cauchy Problem

<i>α</i>-Times Integrated C Semigroups and Strong Solution of Abstract Cauchy Problem