In this paper, we introduce the concept of Stepanov-like (weighted) pseudo S-asymptotically Bloch type periodic processes in the square mean sense, and establish some basic results on the function space of such processes like completeness, convolution and composition theorems. Under the situation that the functions forcing are Stepanov-like (weighted) pseudo S-asymptotically Bloch type periodic and verify some suitable assumptions, we establish the existence and uniqueness of square-mean (weighted) pseudo S-asymptotically Bloch type periodic mild solutions of some fractional stochastic integrodifferential equations (driven by fractional Brownian motion). Finally, the most important findings are substantiated with the assistance of an illustration.

本文介绍了平方均值意义上的类Stepanov（加权）伪S-渐近Bloch型周期过程的概念，并在此类过程的函数空间上建立了完备性、卷积和复合定理等基本结果。在函数强迫为类Stepanov（加权）伪S-渐近Bloch型周期的情况下，并验证了一些适当的假设，建立了平方均值（加权）伪S-渐近Bloch型周期温和解的存在性和唯一性一些分数随机积分微分方程（由分数布朗运动驱动）。最后，最重要的发现通过插图得到证实。