<p>In this paper, we address the problem of identifying the initial value and source term of the non-homogeneous Rayleigh-Stokes equation for a generalized second-grade fluid, modeled by the Riemann-Liouville fractional derivative. This inverse problem is ill-posed; therefore, the Landweber regularization method is employed to solve it. Additionally, convergence estimates between the exact solution and the regularized solution are presented using a-priori and a-posteriori parameter choice rules, based on a conditional stability result. To verify the efficiency of the proposed method, several representative numerical examples are constructed.</p>