Regularization of backward time-space-fractional parabolic equations by quasi-reversibility method

This paper investigates the quasi-reversibility, a regularization method for backward time-space-fractional parabolic equations. Error estimates of Hölder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable noniterative numerical scheme. The theoretical error estimates are confirmed with numerical tests for one and two-dimensional equations.