THE PROBLEM OF CHOOSING THE TYPE OF DERIVATIVES OF FRACTIONAL ORDER FOR PERIODIC FUNCTIONS

UDC 517.948

 

Ponomareva Svetlana Vladamirovna − PhD (Physics and Mathematics), Assistant Professor, the Department of Functional Analysis and Analytical Economics. Belarusian State University (4, Nezavisimosti Ave., 220050, Minsk, Republic of Belarus). E-mail: demyanko@bsu.by Pyzhkova Olga Nikolaevna − PhD (Physics and Mathematics), Head of the Department of Higher Mathematics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: olga.pyzhcova@gmail.com Romashchenko Galyna Stanislavovna − PhD (Physics and Mathematics), Assistant Professor, the Department of Functional Analysis and Analytical Economics. Belarusian State University (4, Nezavisimosti Ave., 220050, Minsk, Republic of Belarus). E-mail: gal.romash@gmail.com

 

DOI: https://doi.org/ 10.52065/2520-6141-2023-272-2-1.

 

Key words: : fractional derivative, integral operator of fractional order, periodic functions.

 

For citation: Ponomareva S. V., Pyzhkova O. N., Romashchenko G. S. The problem of choosing the type of derivatives of fractional order for periodic functions. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2023, no. 2 (272), pp. 5–8. DOI: 10.52065/2520-6141-2023-272-2-1 (In Russian).

 

Abstract

Various non-equivalent definitions of fractional integration (fractional differentiation) operations proposed by Weil, Riemann ‒ Liouville, Hadamard, Grunwald ‒ Letnikov, Marchaux are considered. The choice of the construction of a fractional integral (fractional derivative) is due to the convenience of solving a specific problem and leads to the appearance of important properties on the classes of some functions. On the other hand, the design often leads to certain «disadvantages», which are described in the work. It is shown that on the set of periodic functions summable to the pth power, these definitions are equivalent.

 

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References

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Поступила после доработки 15.03.2023