In this paper, we study a fractional nonlinear Rayleigh–Stokes problem with final value condition. By means of the finite dimensional approximation, we first obtain the compactness of solution operators. Moreover, we handle the problem in weighted continuous function spaces, and then the existence result of solutions is established. Finally, because of the ill posedness of backward problem in the sense of Hadamard, the quasi-boundary value method is utilized to get the regularized solutions, and the corresponding convergence rate is obtained.

中文翻译：

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具有最终条件的非线性分数Rayleigh-Stokes问题解的存在性和正则化

在本文中，我们研究了具有终值条件的分数阶非线性 Rayleigh-Stokes 问题。通过有限维近似，我们首先得到解算子的紧致性。此外，我们在加权连续函数空间中处理问题，然后建立解的存在性结果。最后，针对Hadamard意义上的后向问题的不适定性，利用拟边值法得到正则化解，得到相应的收敛速度。