# Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 39. no. 2. pp. 62–77. ISSN 2079-6641

**MSC 35G15; 35L35 **

**Research Article**

**On a control problem for the subdiffusion equation with a fractional derivative in the sense of Caputo**

**Yu. E. Fayziev**

National University of Uzbekistan Uzbekistan, 100174, Tashkent city, university campus, Republic of Uzbekistan.

E-mail: fayziev.yusuf@mail.ru

In the rectangle for a differential equation of fractional order in the sense of Caputo, we study the control problem with the help of a source function. In other words, the task is to find the source function f(x;y) in such a way that, as a result, at the time t = Θ the temperature of the object under study should be distributed as a given function Ψ(x;y). Sufficient conditions are found for the function Ψ(x;y), which ensure both the existence and uniqueness of the solution to the control problem.

*Key words: fractional derivatives in the sense of Caputo, heat conduction equations, control problem.*

**DOI: 10.26117/2079-6641-2022-39-2-62-77**

**Original article submitted: 20.06.2022 **

**Revision submitted: 12.08.2022**

**For citation.** Fayziev Yu. E. On one control problem for the equationOn a control problem for the subdiffusion equation with a fractional derivative in the sense of Caputo. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 39: 2, 62-77. DOI: 10.26117/2079-6641-2022-39-2-62-77

**Competing interests.** The authors declare that there are no conflicts of interest regarding authorship and publication.

**Contribution and Responsibility.** All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Fayziev Yu. E., 2022

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**F**** ayziev Yusuf Ergashevich** – PhD (Phys. & Math.), Associate Professor, Faculty of Physics and Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan, ORCID 0000-0002-8361-2525.