Generalized Tikhonov method for the final value problem of time-fractional diffusion equation

ABSTRACT

This paper investigates the final value problem for a time-fractional diffusion equation. We determine the initial data from a noisy final data. A generalized Tikhonov regularization method is proposed to deal with this ill-posed problem, and then the convergence rates is derived by the a-priori and a-posteriori choice rules of regularization parameter. A numerical example is presented to show that this method is stable and feasible.

KEYWORDS:

• time-fractional diffusion equation
• final value problem
• generalized Tikhonovregularization
• convergence estimate
• a-priori and a-posteriori parameter selections

2010 AMS Subject Classifications:

• 35R11
• 35R30

Acknowledgments

The authors would like to thank the reviewers for their constructive comments and valuable suggestions that improve the quality of our paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The work described in this paper was supported by the NSF of China (11371181), the SRF (2014XYZ08), NFPBP (2014QZP02) of Beifang University of Nationalities, the SRP of Ningxia Higher School (NGY20140149) and SRP of State Ethnic Affairs Commission of China (14BFZ004).