非线性随机泛函发展方程是数学、物理学、经济学、生物学、工程控制等学科研究的热点之一。本项目计划研究由分数阶Brownian运动驱动的非线性非自治随机泛函发展方程温和解的存在唯一性、稳定性、吸引子以及不变流形问题，其中包括Hurst参数为 [1/2，1）和（1/3，1/2）两种情形。首先运用推广的Lebesgue-Stieltjes积分（或者Young积分）理论来定义随机积分，结合Banach不动点定理，给出该系统温和解的局部存在唯一性。然后，通过建立一个比较原理和利用截距法，获得该方程温和解的全局存在唯一性。紧接着，利用微分积分不等式获得该全局温和解的指数估计。最后，结合一些已知的结论，证明该随机泛函发展方程吸引子和不变流形的存在性。本项目来源于实际问题，具有重要的理论意义与应用价值。

Nonlinear stochastic functional evolution equations have been studied extensively over the recent decades and have been widely applied within various engineering and scientific fields, including mathematics, mechanics, economics, population biology, and control theory. This project is mainly concerned with the existence, uniqueness, stability, attractor and invariant manifold for nonlinear nonautonomous stochastic functional evolution equations driven by fractional Brownian motion, where the Hurst parameter H may belong to [1/2,1) or (1/3,1/2). Firstly, using the generalized Lebesgue-Stieltjes integral (or Young integral) theory to define the stochastic integral for fractional Brownian motion, combing with the classical Banach fixed point theorem, the local existence and uniqueness of the mild solution for this system will be obtained. Secondly, the existence-uniqueness theorem of the global mild solution will be given by establishing an comparison principle and effectively utilizing the piecewise method. Thirdly, an exponential estimate of the global mild solution will be established by constructing a delay inequality. Finally, employing some known results, the existence of random attractor and invariant manifold will be proofed. Since this project arises from many practical problems, it has a very important theoretical significance and application value.