Abstract

In this study, fractional stochastic pseudo-parabolic equations driven by fractional Brownian motion are investigated. This work aims at establishing existence, uniqueness, regularity results for mild solutions to an initial value problem for considered equations in two cases of H that are $H>\frac{1}{2}$ and $H<\frac{1}{2}.$ In addition, the continuities of mild solutions with respect to the time variable and the order fractional derivative are constructed.

中文翻译：

---

分数阶导数和分数布朗运动的随机伪抛物方程

摘要

在这项研究中，研究了分数布朗运动驱动的分数随机伪抛物方程。这项工作的目的是在两种情况建立温和解的存在性，唯一性，规律性的结果为初始值问题的考虑方程^ h是$H>\frac{\mathrm{1个}}{\mathrm{2个}}$ 和 $H<\frac{\mathrm{1个}}{\mathrm{2个}}。$ 另外，构造了关于时间变量和阶数分数阶导数的温和解的连续性。