Regularization for a Sideways Problem of the Non-Homogeneous Fractional Diffusion Equation

In this article, we investigate a sideways problem of the non-homogeneous time-fractional diffusion equation, which is highly ill-posed. Such a model is obtained from the classical non-homogeneous sideways heat equation by replacing the first-order time derivative by the Caputo fractional derivative. We achieve the result of conditional stability under an a priori assumption. Two regularization strategies, based on the truncation of high frequency components, are constructed for solving the inverse problem in the presence of noisy data, and the corresponding error estimates are proved.

Automated summary

In this article, we investigate a sideways problem of the non-homogeneous time-fractional diffusion equation and obtain conditional stability results. We propose two regularization strategies for solving the inverse problem in the presence of noisy data and prove corresponding error estimates.