Modified Gerasimov –Caputo Formula
- Autores: Volosova N.K.1, Volosov K.A.2, Volosova A.K.2, Karlov M.I.3, Pastukhov D.F.4, Pastukhov Y.F.4
-
Afiliações:
- Bauman Moscow State Technical University
- Russian University of Transport
- Moscow University of Physics and Technology
- Polotsk State University
- Edição: Nº 1 (64) (2024)
- Páginas: 5-14
- Seção: 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
Citar
Texto integral
Resumo
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.
Sobre autores
N. Volosova
Bauman Moscow State Technical University
Autor responsável pela correspondência
Email: navalosova@yandex.ru
Post-graduate Student 2nd Baumanskaya St., 5-1, Moscow, 105005, Russia
K. 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. 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. 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. 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. 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
Bibliografia
- Korchagina, A.N. (2014), "The use of fractional derivatives to solve problems in continuum mechanics", Proceedings of the Altai State University, no. 1–1(81), pp. 65-67. doi: 10.14258/izvasu(2014)1.1-14. EDN SECUCD.
- Nakhushev, A.M. (2003), "Fractional calculus and its application", M., FIZMATLIT, 272 p.
- Beshtokova, Z., Beshtokov, M.Kh. (2021), "Vstability and convergence of monotone difference schemes that approximate boundary value problems for an integro-differential equation with a time-fractional derivative and the Bessel operator / Z.V. Beshtokova", Differential equations and control processes, no. 3, pp. 26-50. EDN GMBWPR.
- Beshtokov, M.Kh. (2020), "Boundary value problems for the loaded modified fractional order moisture transfer equation with the Bessel operator and difference methods for their solution", Bulletin of the Udmurt University. Mathematics. Mechanics. Computer Science, vol. 30, no. 2, pp. 158-175. doi: 10.35634/vm200202. EDN HMCSFN.
- Alieva, S., Mansimov, K.B. (2023), "Toptima-lity condition of the type of Pontryagin's maximum principle in the problem of controlling linear difference equations of fractional order". Bulletin of Perm University. Mathematics. Mechanics. Computer Science, no. 4(63), pp. 5-11. doi: 10.17072/1993-0550-2023-4-5-11. EDN ACKUPX.
- Mansimov, K.B., Bakhmedova, Z.H. (2022), "An analogue of the Pontryagin maximum principle in the problem of optimal control of a system of differential equations with the Caputo fractional derivative and a multipoint quality criterion", Bulletin of Perm University. Mathematics. Mechanics. Computer Science, no. 3(58), pp. 5-10. doi: 10.17072/1993-0550-2022-3-5-10. EDN THSSNA.
- Faddeev, D.K. (1984), "Lectures on algebra: Textbook for universities", M., Science, Fizmatlit, 416 p.
- Bakhvalov, N.S., Lapin, A.V., Chizhonkov, E.V. (2010), "Numerical methods in problems and exercises", M., BINOM, knowledge laboratory, 240 p.
- Pastukhov, D.F., Pastukhov, Y.F., Volosova, N.K., Volosov, K.A., Volosova, A.K. (2020), "Calculation of production of the debrief order with hign accuracy", Novopolotsk, PGU, 21 p. URL: hhtps://elib.psu.by/handle/123456789 /25335.
- Gerber, A.D. (2021), "Description of the algorithm for approximate calculation of an improper integral that determines the values of the fractional derivative", Mathematics and natural sciences. theory and practice: Interuniversity collection of scientific papers, Yaroslavl, Yaroslavl State Technical University, vol. 16, pp. 22-31. EDN CYCCAJ.
Arquivos suplementares
