标题：An inverse problem of parameter estimation for time-fractional heat conduction in a composite medium using carbon-carbon experimental data
作者：Zhuang, Qiao; Yu, Bo; Jiang, Xiaoyun
作者机构：[Zhuang, Qiao; Yu, Bo; Jiang, Xiaoyun] Shandong Univ, Sch Math, Jinan 250100, Peoples R China.
通讯作者地址：[Jiang, XY]Shandong Univ, Sch Math, Jinan 250100, Peoples R China.
来源：PHYSICA B-CONDENSED MATTER
关键词：Inverse problem; Parameter estimation; Time-fractional heat conduction;; Composite medium; Caputo fractional derivative
摘要：In this paper, a time-fractional heat conduction problem is mathematically proposed for an experimental heat conduction process in a 3-layer composite medium. A numerical solution to the direct problem is obtained with finite difference method. In regard to the inverse problem, the optimal order of Caputo fractional derivative is estimated with Levenberg-Marquardt method. Comparing with the carbon-carbon experimental data, the results show that the time-fractional heat conduction model provides an effective and accurate simulation of the experimental data. The rationality of the proposed time-fractional model and validity of Levenberg-Marquardt method in solving the time-fractional inverse heat conduction problem are also manifested according to the results. By conducting the sensitivity analysis, the feasibility of the parameter estimation is further discussed. (C) 2014 Elsevier B.V. All rights reserved.