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

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.

Keywords:

• Fractional Landweber
• regularization
• fractional wave

2010 Mathematics Subject Classification:

• 35R11

Acknowledgments

This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2019.09.

Disclosure statement

No potential conflict of interest was reported by the authors.