Abstract In this paper we study subordination principles for fractional differential equations of Sobolev type in Banach space. With the help of the theory of Sobolev type resolvent families (known also as propagation family) as well as these subordination principles, we obtain the existence of mild solutions for this kind of equations. We study simultaneously the case 0 < α < 1 and 1 < α < 2 for the Caputo and Riemann-Liouville fractional derivatives.

中文翻译：

---

Sobolev型分数阶扩散波方程的从属原理

摘要 本文研究了Banach空间中Sobolev型分数阶微分方程的从属原理。借助Sobolev型求解器族（也称为传播族）理论以及这些从属原理，我们得到了这类方程的温和解的存在性。我们同时研究了 Caputo 和 Riemann-Liouville 分数阶导数的情况 0 < α < 1 和 1 < α < 2。