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A backward problem for the time‐fractional diffusion equation
Author(s) -
AlJamal Mohammad F.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4151
Subject(s) - tikhonov regularization , mathematics , eigenfunction , uniqueness , regularization (linguistics) , inverse problem , diffusion equation , stability (learning theory) , mathematical analysis , diffusion , eigenvalues and eigenvectors , computer science , physics , economy , quantum mechanics , artificial intelligence , machine learning , economics , service (business) , thermodynamics
In this paper, we are concerned with the backward problem of reconstructing the initial condition of a time‐fractional diffusion equation from interior measurements. We establish uniqueness results and provide stability analysis. Our method is based on the eigenfunction expansion of the forward solution and the Tikhonov regularization to tackle the ill‐posedness issue of the underlying inverse problem. Some numerical examples are included to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.