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Inverse Problem of Determining an Order of the Riemann-Liouville Time-Fractional Derivative |
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PP: 467-474 |
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doi:10.18576/pfda/080401
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Author(s) |
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Shavkat Alimov,
Ravshan Ashurov,
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Abstract |
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| It is considered the inverse problem of identification the order ρ of the fractional Riemann - Liouville derivative in time in the abstract subdiffusion equation, the elliptical part of which is a self-adjoint positive operator with a discrete spectrum. It is proved that the norm ||u(t )|| of the solution at a fixed t = t0 restores uniquely the order ρ . At the same time, an interesting effect was discovered: for sufficiently large t, the norm ||u(t)||, considered as a function of ρ, is monotolically decreasing. A number of examples of concrete subdiffusion equations are discussed.
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