"Inverse Problem of Determining an Order of the Riemann-Liouville Time-" by Shavkat Alimov and Ravshan Ashurov

Progress in Fractional Differentiation & Applications

Article Title

Inverse Problem of Determining an Order of the Riemann-Liouville Time-Fractional Derivative

Authors

Shavkat Alimov, Department of Mathematics, National University of Uzbekistan, Tashkent, UzbekistanFollow
Ravshan Ashurov, Laboratory of Differential Equations and their Applications, Institute of Mathematics of the Academy of Sciences, Tashkent, UzbekistanFollow

Author Country (or Countries)

Uzbekistan

Abstract

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080401

Recommended Citation

Alimov, Shavkat and Ashurov, Ravshan (2022) "Inverse Problem of Determining an Order of the Riemann-Liouville Time-Fractional Derivative," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 4, Article 1.
DOI: http://dx.doi.org/10.18576/pfda/080401
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss4/1

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