标题： 直接和逆向的具有几乎扇形算子分数次幂的抽象柯西问题 显示英文标题

标题： Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators

摘要： 我们展示了涉及时变系数和几乎扇形算子的分数次幂的抽象柯西问题的显式解算子。 同时，通过解算子的表示，我们解决了逆抽象柯西问题以恢复时变系数。 作为补充，我们还研究了使用依赖于时变的几乎扇形算子的类似问题。 显示英文摘要

摘要： We show the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. Also, by using the representation of the solution operator, we solve the inverse abstract Cauchy problem for recovering the time-variable coefficient. As a complement, we also study similar problems by using almost sectorial operators that depend on a time-variable.