A potential-free field inverse time-fractional Schrödinger problem: optimal error bound analysis and regularization method
• Fan Yang,
• Junliang Fu,
• Xiao-Xiao Li
Fan Yang
LanZhou University of Technology
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Junliang Fu
Lanzhou University of Technology
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Xiao-Xiao Li
LanZhou University of Technology
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## Abstract

In this paper, an inverse time-fractional Schr$\ddot{o}$dinger problem of potential-free field is studied. This problem is ill-posed, i.e, the solution (if it exists) does not depend continuously on the data. Based on an a priori bound condition, the optimal error bound analysis is given. Moreover, a modified kernel method is introduced. The convergence error estimate obtained by this method under the priori regularization parameter selection rule is optimal, and the convergence error estimate obtained under the posteriori regularization parameter selection rule is order-optimal. Finally, some numerical examples are given to illustrate the effectiveness and stability of this method.

#### Peer review status:ACCEPTED

23 Apr 2020Submitted to Mathematical Methods in the Applied Sciences
25 Apr 2020Submission Checks Completed
25 Apr 2020Assigned to Editor
29 Apr 2020Reviewer(s) Assigned
25 Jul 2020Review(s) Completed, Editorial Evaluation Pending
28 Jul 2020Editorial Decision: Revise Minor
09 Aug 20201st Revision Received
09 Aug 2020Submission Checks Completed
09 Aug 2020Assigned to Editor
09 Aug 2020Editorial Decision: Accept