A hybrid regularization method for identifying the source term and the initial value simultaneously for fractional pseudo-parabolic equation with involution

In this paper, we study the problem of identifying source term and initial value simultaneously for fractional pseudo-parabolic equation with involution. This is an ill-posed problem and the conditional stability is given. A hybrid regularization method, which combines the modified quasi-inverse and the modified quasi-initial value, is used to deal with the inverse problem. The error estimates of the exact solutions and the regularization solutions are given respectively under the priori and the posteriori regularization parameter choice rules. Several numerical examples are presented to certify the hybrid regularization method is effective.