PARAMETER IDENTIFICATION IN FRACTIONAL DIFFERENTIAL EQUATIONS  

作　　者：李景 郭柏灵 

机构地区：[1]School of Mathematics and Computational Science, Changsha University of Science and Technology [2]Institute of Applied Physics and Computational Mathematics

出　　处：《Acta Mathematica Scientia》2013年第3期855-864,共10页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (11226166 and 11001033);Scientific Research Fund of Hunan Provinical Education (11C0052)

摘　　要：This article investigates the fractional derivative order identification, the coefficient identification, and the source identification in the fractional diffusion problems. If 1 〈 α〈 2, we prove the unique determination of the fractional derivative order and the dif- fusion coefficient p（x） by fo u（0, s）ds, 0 〈 t 〈 T for one-dimensional fractional diffusion-wave equations. Besides, if 0 〈 α 〈 1, we show the unique determination of the source term f（x, y） by U（0, 0, t）, 0 〈 t 〈 T for two-dimensional fractional diffusion equations. Here, a denotes the fractional derivative order over t.This article investigates the fractional derivative order identification, the coefficient identification, and the source identification in the fractional diffusion problems. If 1 〈 α〈 2, we prove the unique determination of the fractional derivative order and the dif- fusion coefficient p（x） by fo u（0, s）ds, 0 〈 t 〈 T for one-dimensional fractional diffusion-wave equations. Besides, if 0 〈 α 〈 1, we show the unique determination of the source term f（x, y） by U（0, 0, t）, 0 〈 t 〈 T for two-dimensional fractional diffusion equations. Here, a denotes the fractional derivative order over t.

关 键 词：Fractional differential equation inverse problems parameter identification 

分 类 号：O175[理学—数学]