NAYMARK PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION WITH A FRACTIONAL DISCRETE DISTRIBUTED DIFFERENTIATION OPERATOR

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

For an ordinary differential equation with a fractional discretely distributed differentiation operator, the Naimark problem is studied, where the boundary conditions are specified in the form of linear functionals. This allows us to cover a fairly wide class of linear local and nonlocal conditions. A necessary and sufficient condition for the unique solvability of the problem is obtained. A representation of the solution to the problem under study is found in terms of special functions. The theorem of existence and uniqueness of the solution is proven.

作者简介

L. Gadzova

Kabardin-Balkar Scientific Center of RAS

Email: macaneeva@mail.ru
Nalchik, Russia

参考

  1. Nakhushev, A.M., Drobnoye ischisleniye i yego primeneniye (Fractional Calculus and its Applications), Moscow: Fizmatlit, 2003.
  2. Pskhu, A.V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka (Fractional Partial Differential Equations), Moscow: Nauka, 2005.
  3. Pskhu, A. Transmutation operators intertwining first-order and distributed-order derivatives / A. Pskhu // Bol. Soc. Mat. Mex. — 2023. — V. 29, № 93.
  4. Pskhu, A.V. Transmutations for multi-term fractional operators / A.V. Pskhu // Transmutation Operators and Applications. Trends in Mathematics ; eds. V. Kravchenko, S. Sitnik. — Cham : Birkhauser, 2020. — P. 603-614.
  5. Fedorov, V.E. On strongly continuous resolving families of operators for fractional distributed order equations / V.E. Fedorov, N.V. Filin // Fractal Fract. — 2021. — V. 5, № 1. — Art. 20.
  6. Analytic resolving families for equations with distributed Riemann-Liouville derivatives / V.E. Fedorov, W.Sh. Du, M. Kostic, A.A. Abdrakhmanova // Mathematics. — 2022. — V. 10, № 5. — Art. 681.
  7. On the solvability of equations with a distributed fractional derivative given by the Stieltjes integral / S.M. Sitnik, V.E. Fedorov, N.V. Filin, V.A. Polunin // Mathematics. — 2022. — V. 10, № 16. — Art. 2979.
  8. Efendiev, B.I., Initial-value problem for a second-order ordinary differential equation with distributed-order differentiation operator, Math. Notes of NEFU, 2022, vol. 29, no. 2, pp. 59–71.
  9. Efendiev, B.I., Lyapunov inequality for second-order equation with operator of distributed differentiation, Math. Notes, 2023, vol. 113, no. 5-6, pp. 879–882.
  10. Gadzova, L.Kh., Dirichlet and Neumann problems for a fractional ordinary differential equation with constant coefficients, Differ. Equat., 2015, vol. 51, no. 12, pp. 1556–1562.
  11. Gadzova, L.Kh., Boundary value problem for a linear ordinary differential equation with a fractional discretely distributed differentiation operator, Differ. Equat., 2018, vol. 54, no. 2, pp. 178–184.
  12. Gadzova, L.Kh., Nonlocal boundary-value problem for a linear ordinary differential equation with fractional discretely distributed differentiation operator, Math. Notes, 2019, vol. 106, no. 5–6, pp. 904–908.
  13. Gadzova, L.Kh. Generalized boundary value problem for a linear ordinary differential equation with a fractional discretely distributed differentiation operator / L.Kh. Gadzova // Bull. Karaganda Univ. Math. Ser. — 2022. — V. 106, № 2. — P. 108-116.
  14. Wright, E.M. On the coefficients of power series having exponential singularities / E.M. Wright // J. London Math. Soc. — 1933. — V. 8, № 29. — P. 71-79.
  15. Gadzova, L.Kh., Zadacha Koshi dlya obyknovennogo differentsial’nogo uravneniya s operatorom drobnogo diskretno raspredelennogo differentsirovaniya, Vest. KRAUNTS. Fiz.-mat. nauki, 2018, vol. 3, no. 23, pp. 48–56.

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2024