Regularization of nonlocal pseudo-parabolic equation with random noise

Abstract

In this paper, we consider an inverse problem for a time-fractional diffusion equation with the inhomogeneous source. These problems have many applications in engineering such as image processing, geophysics, biology. We get the result in random case as follows: • This problem is ill-posed. • We have used the nonlocal condition, instead of the final time condition. • Using the IFT regularization method, constructing the regularized solution, the a-priori choice rule for the regularization parameter is discussed and yields the corresponding convergence rate. • A numerical experiment is presented to illustrate the results in theory.