The quasi-reversibility method for a final value problem of the time-fractional diffusion equation with inhomogeneous source

This paper is devoted to discuss a multidimensional backward heat conduction problem for time-fractional diffusion equation with inhomogeneous source. This problem is ill-posed. We use quasi-reversibility regularization method to solve this inverse problem. Moreover, the convergence estimates between regularization solution and the exact solution are obtained under the a priori and the a posteriori choice rules. Finally, the numerical examples for one-dimensional and two-dimensional cases are presented to show that our method is feasible and effective.