We are devoted with fractional abstract Cauchy problems. Required conditions on spaces and operators are given guaranteeing existence and uniqueness of solutions. An inverse problem is also studied. Applications from partial differential equations are given to illustrate the abstract fractional degenerate differential problems.

中文翻译：

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无限区间情况下的分数柯西问题

我们致力于分数抽象柯西问题。给出了空间和算子的必要条件，以保证解的存在和唯一性。还研究了反问题。偏微分方程的应用被给出来说明抽象分数退化简并微分问题。