In this paper we investigate the existence, asymptotic behavior and uniform $p$-integrability of fractional resolvent families generated by sectorial operators in Banach spaces. As a consequence, we obtain properties on the behavior of mild solutions to abstract fractional Cauchy problems for the Caputo and Riemann–Liouville fractional derivatives.

中文翻译：

---

Banach空间中分数次柯西问题的温和解的渐近行为

在本文中，我们研究了存在性，渐近行为和均匀性 $p$-Banach空间中部门算子生成的分数分解物族的可积性。结果，我们获得了Caputo和Riemann-Liouville分数阶导数抽象分数次柯西问题的温和解的性质。