Modified fractional Landweber iterative method for the source identification problem of pseudo-parabolic equation

This article studies a source identification problem of a fractional pseudo-parabolic equation in which the identified source depends on the spatial variable. Based on the ill-posedness analysis, we first establish a conditional stability result of Hölder type for this problem. Then, by combining with the fractional Landweber iteration method and Fourier truncation technique, we construct a modified fractional Landweber iterative regularization method to restore the stability of the solution on the noisy data. Meanwhile, under the a priori and a posteriori selection rules for the regularization parameter, we give and prove the convergence estimates of Hölder type for the regularization method. Finally, some numerical examples and simulation results are provided to verify the stability and feasibility of this regularization method.