Geodesic
On a nonlocal boundary value problem
News of the Kabardin-Balkar scientific center of RAS, no. 3 (2020), pp. 5-12 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we study a nonlocal boundary value problem for a generalized telegraph equation with fractional derivatives. Fractional differentiation is specified using the Caputo operator. The equation is considered in a bounded rectangular domain of the plane of two independent variables. Nonlocal boundary conditions are specified in the form of partial integral expressions from the desired solution for each of the variables with given continuous kernels. Using the previously obtained representation for the solution of the Goursat problem for the equation under study in terms of the Wright-type function, the problem under consideration can be reduced to the system of Volterra linear integral equations with respect to the traces of the desired solution on the part of the boundary of the domain. As a result, a theorem on the existence and uniqueness of a solution to the problem under study is proved; its representation is found in terms of solutions to the resulting system of integral equations.
Keywords: non-local problem, Caputo derivative, fractional telegraph equation, integral condition, Wright-type function. 
@article{IZKAB_2020_3_a0,
     author = {R. A. Pshibikhova},
     title = {On a nonlocal boundary value problem},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {5--12},
     year = {2020},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IZKAB_2020_3_a0/}
}
TY  - JOUR
AU  - R. A. Pshibikhova
TI  - On a nonlocal boundary value problem
JO  - News of the Kabardin-Balkar scientific center of RAS
PY  - 2020
SP  - 5
EP  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IZKAB_2020_3_a0/
LA  - ru
ID  - IZKAB_2020_3_a0
ER  - 
%0 Journal Article
%A R. A. Pshibikhova
%T On a nonlocal boundary value problem
%J News of the Kabardin-Balkar scientific center of RAS
%D 2020
%P 5-12
%N 3
%U http://geodesic.mathdoc.fr/item/IZKAB_2020_3_a0/
%G ru
%F IZKAB_2020_3_a0
R. A. Pshibikhova. On a nonlocal boundary value problem. News of the Kabardin-Balkar scientific center of RAS, no. 3 (2020), pp. 5-12. http://geodesic.mathdoc.fr/item/IZKAB_2020_3_a0/

[1] A. M. Nakhushev, Fractional calculus and its application, Fizmatlit, M., 2003, 272 pp.

[2] R. C. Cascaval, E. C. Eckstein, C. L. Frota, J. A. Goldstein, “Fractional telegraph equations”, Journal of Mathematical Analysis and Applications, 276:1 (2002), 145–159 | DOI | MR | Zbl

[3] A. V. Pskhu, “A boundary value problem for a fractional differential equation with partial derivatives”, News of the Kabardino-Balkarian Scientific Center of the RAS, 2002, no. 1, 76–78

[4] M. O. Mamchuev, “General representation of solutions of the fractional telegraph equation”, Reports of Adyghe (Circassian) International Academy of Sciences, 16:2 (2014), 47–51

[5] R. A. Pshibikhova, “An analogue of the Goursat problem for a generalized telegraph equation of fractional order”, Differential equations, 50:6 (2014), 839–843 | MR | Zbl

[6] A. S. Eremin, “Three problems for a single partial fractional equation”, Differential equations and boundary value problems, Proceedings of the All-Russian Scientific Conference, v. 3, Mathematical modeling and boundary value problems, Samara State Technical University, Samara, 2004, 94–98

[7] R. A. Pshibikhova, “The Goursat problem for a fractional telegraph equation with Caputo derivatives and with an integral condition”, News of the Kabardino-Balkarian Scientific Center of the RAS, 2016, no. 4 (70), 25–29 | MR

[8] R. A. Pshibikhova, “The Goursat problem for a fractional telegraph equation with Caputo derivatives”, Mathematical Notes, 99:4 (2016), 559–563 | MR

[9] A. V. Pskhu, Partial differential equations of fractional order, Science, M., 2005, 199 pp.

[10] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud., Amsterdam, 2006, 204 pp. | MR | Zbl

[11] V. I. Smirnov, Course in higher mathematics, v. 5, Fiz-matgiz, M., 1959 | MR