Fractional Landweber method for an initial inverse problem for time-fractional wave equations

Abstract

ABSTRACT In this paper, we consider the initial inverse problem (backward problem) for an inhomogeneous time-fractional wave equation in a general bounded domain. We show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Landweber regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.