Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation. (16th April 2021)

• Record Type: Journal Article
• Authors: Sun, L L; Li, Y S; Zhang, Y
• Is Part Of: Inverse problems. Volume 37:Number 5(2021)
• Publication Date: 2021-04-16
• Subjects: time-fractional diffusion equation -- inverse problems -- inversion of potential -- inversion of fractional orders -- multinomial Mittag-Leffler function -- Levenberg–Marquardt method -- uniqueness; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abf162
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In the present paper, we devote our effort to a nonlinear inverse problem for simultaneously recovering the potential function and the fractional orders in a multi-term time-fractional diffusion equation from the noisy boundary Cauchy data in the one-dimensional case. The uniqueness for the inverse problem is derived based on the analytic continuation, the Laplace transformation and the Gel'fand–Levitan theory. Finally, the Levenberg–Marquardt regularization method with a regularization parameter chosen by a sigmoid-type function is applied for finding a stable approximate solution. Three numerical examples are provided to show the effectiveness of the proposed method.