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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 3204959, 7 pages
https://doi.org/10.1155/2017/3204959
Research Article

Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE

1School of Science, Shandong University of Technology, Zibo 255049, China
2Department of Mathematics, Southeast University, Nanjing 210096, China

Correspondence should be addressed to Gongsheng Li; nc.ude.tuds@sgil

Received 9 February 2017; Accepted 2 July 2017; Published 17 August 2017

Academic Editor: Ming Mei

Copyright © 2017 Chunlong Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short) from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data give good approximations to the exact order demonstrating the efficiency of the inversion algorithm and numerical stability of the inversion problem.