Abstract An fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

中文翻译：

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复杂插值尺度上的分数抽象柯西问题

摘要 研究了扇形算子产生的分数抽象柯西问题。建立了一个矫顽力类型的不等式，该不等式对于由具有相同参数的扇形算子生成的复插值尺度的解。显示了在具有分数时间导数的有界域中微分抛物线初始边界值问题的应用。