Modified Gerasimov –Caputo Formula
- Authors: Volosova N.K.1, Volosov K.A.2, Volosova A.K.2, Karlov M.I.3, Pastukhov D.F.4, Pastukhov Y.F.4
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Affiliations:
- Bauman Moscow State Technical University
- Russian University of Transport
- Moscow University of Physics and Technology
- Polotsk State University
- Issue: No 1 (64) (2024)
- Pages: 5-14
- Section: Mathematics
- URL: https://journal-vniispk.ru/1993-0550/article/view/307264
- DOI: https://doi.org/10.17072/1993-0550-2024-1-5-14
- ID: 307264
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Abstract
In this work, modified Gerasimov–Caputo formulas were obtained for the first time. The modified formulas take into account the value of the derivative of the function at zero with an order of one less than the order of the derivative under the sign of the Gerasimov–Caputo integral. Without taking into account the new term in the Gerasimov–Caputo formulas, it is not always possible to calculate the fractional derivative on any order interval and for any function. The paper also describes a simple numerical algorithm with the Gaussian quadrature formula, which allows one to calculate the fractional derivative with double precision. tables of fractional derivatives for the sine and cosine functions have been compiled. Moreover, the first half of the tables (in the interval of order (0,1)) and the second half of the tables (in the interval of order (1,2)) were obtained by programs using different algorithms. In the work, an absolute error in calculating the fractional derivative of 10–15 was achieved.
About the authors
N. K. Volosova
Bauman Moscow State Technical University
Author for correspondence.
Email: navalosova@yandex.ru
Post-graduate Student 2nd Baumanskaya St., 5-1, Moscow, 105005, Russia
K. A. Volosov
Russian University of Transport
Email: konstantinvolosov@yandex.ru
Doctor of Physical and Mathematical Sciences, Professor Obraztsova St., 9-9, Moscow, GSP-4, 127994, Russia
A. K. Volosova
Russian University of Transport
Email: alya01@yandex.ru
Candidate of Physical and Mathematical Sciences, Chief Analytical Department "Tramplin" LLC Obraztsova St., 9-9, Moscow, GSP-4, 127994, Russia
M. I. Karlov
Moscow University of Physics and Technology
Email: karlov@shade.msu.ru
Candidate of Physical and Mathematical Sciences, Associate Professor Institutskiy per., 9, Dolgoprudny, 141701, Moscow region, Russia
D. F. Pastukhov
Polotsk State University
Email: dmitrij.pastuhov@mail.ru
Candidate of Physical and Mathematical Sciences, Associate Professor Blokhin St., 29, Novopolotsk, Vitebsk Region, 211440, Republic of Belarus
Yu. F. Pastukhov
Polotsk State University
Email: pulsar1900@mail.ru
Candidate of Physical and Mathematical Sciences, Associate Professor Blokhin St., 29, Novopolotsk, Vitebsk Region, 211440, Republic of Belarus
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