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Recovery of a fractional diffusion equation from a single boundary measurement
Author(s) -
Boumenir Amin,
Kim Tuan Vu
Publication year - 2019
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.5456
Subject(s) - mathematics , fractional calculus , diffusion equation , mathematical analysis , boundary (topology) , constructive , diffusion , inverse , derivative (finance) , inverse problem , geometry , physics , economy , economics , thermodynamics , service (business) , process (computing) , computer science , financial economics , operating system
We prove that we can uniquely recover the coefficient of a one‐dimensional fractional diffusion equation from a single boundary measurement and also provide a constructive procedure for its recovery. The algorithm is based on the well‐known Gelfand‐Levitan inverse spectral theory of Sturm‐Liouville operators. Note that the nonlocal nature of the fractional derivative makes it more difficult to observe the solution and extract the spectral data.