Backward problem for a nonlinear fractional bi-parabolic equation with Gaussian white noise

In this paper, we investigate an approach for regularizing the inverse problem associated with the nonlinear bi-parabolic equation involving the fractional Laplacian. Moreover, we consider the source function satisfying locally Lipschitz condition and the input data are perturbed by Gaussian white noise. We also demonstrate the ill-posedness of the problem, then we use the Fourier truncation method to regularize it and propose the convergence rates between the exact solution and the regularized solution. Numerical examples are provided to illustrate the effectiveness of the theoretical results.