Recovering space-dependent source for a time-space fractional diffusion wave equation by fractional Landweber method

Abstract

In this paper, we consider a problem of recovering a space-dependent source for a time fractional diffusion wave equation by the fractional Landweber method. The inverse problem has been transformed into an integral equation by using the final measured data. We use the fractional Landweber regularization method for overcoming the ill-posedness. We discuss an a-priori regularization parameter choice rule and an a-posteriori regularization parameter choice rule, and we also prove the conditional stability and convergence rates for the inverse problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.

Keywords:

• Fractional diffusion wave equation
• inverse problem
• fractional Landweber method
• convergence estimates
• numerical calculation

2010 Mathematics Subject Classification:

• Inverse Problem

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper was supported by the National Natural Science Foundation (NSF) of China [grant number 11471150].