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Inverse problems for fractional Schrödinger and subdiffusion equations

Authors

  • Ashurov Ravshan Radjabovich Institute of Mathematics named after V.I. Romanovsky
  • Shakarova Marjona Dilshod qizi Institute of Mathematics named after V.I. Romanovsky

DOI:

https://doi.org/10.52754/16948645_2023_1_250

Keywords:

Schrödinger and subdiffusion equation, equation, the Caputo derivatives, Fourier method.

Abstract

The inverse problems of determining the right-hand side of  the Schrödinger and the sub-diffusion equations with the fractional derivative is considered. In the problem 1, the time-dependent source identification problem for the Schrödinger equation , in a Hilbert space  is investigated. To solve this inverse problem, we take the additional condition  with an arbitrary bounded linear functional . In the problem 2, we consider the subdiffusion equation with a fractional derivative of order , and take the аbstract operator as the elliptic part. The right-hand side of the equation has the form , where  is a given function and the inverse problem of determining element is considered. The condition  is taken as the over-determination condition, where  is some interior point of the considering domain and  is a given element. Obtained results are new even for classical diffusion equations. Existence and uniqueness theorems for the solutions to the problems under consideration are proved.

References

Pskhu A.V. Fractional Differential Equations. Moscow: NAUKA. 2005 [in Russian].

Ashyralyev.A., Urun.M. Time-dependent source identification problem for the Schrodinger equation with nonlocal boundary conditions, In: AIP Conf. Proc, V:2183, 2019. DOI: https://doi.org/10.1063/1.5136178

Slodichka M., Sishskova K., Bockstal V. Uniqueness for an inverse source problem of determining a space dependent source in a time-fractional diffusion equation, Appl. Math. Letters, V. 91, pp. 15-21, 2019. DOI: https://doi.org/10.1016/j.aml.2018.11.012

Published

2023-06-30

Versions

How to Cite

Ashurov , R., & Shakarova , M. (2023). Inverse problems for fractional Schrödinger and subdiffusion equations. Journal of Osh State University. Mathematics. Physics. Technical Sciences, (1(2), 250–254. https://doi.org/10.52754/16948645_2023_1_250