Recovery of a fractional diffusion equation from a single boundary measurement
Corresponding Author
Amin Boumenir
Department of Mathematics, University of West Georgia, Carrollton, Georgia
Amin Boumenir, Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA.
Email: [email protected]
Communicated by: D. Zeidan
Search for more papers by this authorVu Kim Tuan
Department of Mathematics, University of West Georgia, Carrollton, Georgia
Search for more papers by this authorCorresponding Author
Amin Boumenir
Department of Mathematics, University of West Georgia, Carrollton, Georgia
Amin Boumenir, Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA.
Email: [email protected]
Communicated by: D. Zeidan
Search for more papers by this authorVu Kim Tuan
Department of Mathematics, University of West Georgia, Carrollton, Georgia
Search for more papers by this authorAbstract
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.
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