Adyghe Int. Sci. J. Vol. 22, No 2. P. 21-28. ISSN 1726-9946

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DOI: https://doi.org/10.47928/1726-9946-2022-22-2-21-28

MATHEMATICS

MSC 32A10; 32A37

Original article

The optimal control problem for the fractional diffusion equation with a derivative in the minimization condition

Mikhail Sergeyevich Ivshin
intern researcher of the Department of Mixed-type Equations Institute of Applied Mathematics and Automation of KBSC RAS (360017, 89~А Shortanova St., Nalchik, Russia), ORCID ID: https://orcid.org/0000-0002-0893-281X, SPIN code: 2054-6207, AuthorID: 1146015, mixail.ivshin.1996@mail.ru

Abstract. Many processes and phenomena in fractal theory and continuum mechanics are described by fractional differential equations, since new fractional models are often more accurate than integer models, that is, these models have more degrees of freedom than the corresponding classical ones. The paper uses the property of the Stankovich transformation of power functions, with the help of which the problem for the fractional diffusion equation was reduced to a system of algebraic equations. It is proved that there is a solution to the problem.

Keywords: fractional calculus, fractional diffusion equation, minimization condition, the polynomial, the Wright function, Stankovich transformation, system of algebraic equations, determinant

Acknowledgments: the author are thankful to the anonymous reviewer for his valuable remakes.

For citation. M. S. Ivshin The optimal control problem for the fractional diffusion equation with a derivative in the minimization condition. Adyghe Int. Sci. J. 2022. Vol. 22, No. 2. P. 21–28.
DOI: https://doi.org/10.47928/1726-9946-2022-22-2-21-28

The author has read and approved the final version of the manuscript.
Submitted 09.06.2022; approved after reviewing 16.06.2022; accepted for publication 22.06.2022.

© Ivshin M. S., 2022

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