Abstract
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.
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