Geodesic
Modified Riemann–Liouville integro-differential operators in the class of harmonic functions and their applications
Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 73-83 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this work we study the properties of some modified integro-differential Riemann–Liouville integro-differential operators. As application of the properties of these operators we consider some local and nonlocal boundary value problems for Laplace equation in a ball. We prove existence and uniqueness for the studied problems. These problems generalize known Dirichlet and Bitsadze–Samarski problems.
Keywords: harmonic function, Bavrin operator, Riemann–Liouville operators, nonlocal problems.
Mots-clés : Laplace equation 
@article{UFA_2015_7_3_a8,
     author = {B. T. Torebek},
     title = {Modified {Riemann{\textendash}Liouville} integro-differential operators in the class of harmonic functions and their applications},
     journal = {Ufa mathematical journal},
     pages = {73--83},
     year = {2015},
     volume = {7},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a8/}
}
TY  - JOUR
AU  - B. T. Torebek
TI  - Modified Riemann–Liouville integro-differential operators in the class of harmonic functions and their applications
JO  - Ufa mathematical journal
PY  - 2015
SP  - 73
EP  - 83
VL  - 7
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a8/
LA  - en
ID  - UFA_2015_7_3_a8
ER  - 
%0 Journal Article
%A B. T. Torebek
%T Modified Riemann–Liouville integro-differential operators in the class of harmonic functions and their applications
%J Ufa mathematical journal
%D 2015
%P 73-83
%V 7
%N 3
%U http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a8/
%G en
%F UFA_2015_7_3_a8
B. T. Torebek. Modified Riemann–Liouville integro-differential operators in the class of harmonic functions and their applications. Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 73-83. http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a8/

[1] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Mathematics studies, North-Holland, 2006, 539 pp. | MR | Zbl

[2] Siberian Advences in Mathematics, 22:2 (2012), 115–134 | DOI | MR | Zbl

[3] Kilbas A. A., Tityura A. A., “Drobnaya proizvodnaya tipa Marsho–Adamara i obraschenie drobnykh integralov”, Doklady Natsionalnoi akademii nauk Belarusi, 50:4 (2006), 5–10 | MR | Zbl

[4] Bavrin I. I., “Operatory dlya garmonicheskikh funktsii i ikh prilozheniya”, Differentsialnye uravneniya, 21:1 (1985), 9–15 | MR | Zbl

[5] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974, 333 pp.

[6] Bavrin I. I., “Integro-differentsialnye operatory dlya garmonicheskikh funktsii v vypuklykh oblastyakh i ikh prilozheniya”, Differentsialnye uravneniya, 24:9 (1988), 1629–1631 | MR | Zbl

[7] Sokolovskii V. B., “Ob odnom obobschenii zadachi Neimana”, Differentsialnye uravneniya, 24:4 (1988), 714–716 | MR

[8] Bitsadze A. V., “K zadache Neimana dlya garmonicheskikh funktsii”, Doklady AN SSSR, 311:1 (1990), 11–13 | MR | Zbl

[9] Karachik V. V., Turmetov B. Kh., “Ob odnoi zadache dlya garmonicheskogo uravneniya”, Izvestiya AN Uz SSR, seriya fiziko-matematicheskikh nauk, 1990, no. 4, 17–21 | MR | Zbl

[10] B. T. Torebek, B. Kh. Turmetov, “On solvability of a boundary value problem for the Poisson equation with the boundary operator of a fractional order”, Boundary Value Problems, 2013 (2013), 93, 18 pp. | DOI | MR | Zbl

[11] Turmetov B. Kh., “Ob odnoi kraevoi zadache dlya garmonicheskogo uravneniya”, Differentsialnye uravneniya, 32:8 (1996), 1089–1092 | MR | Zbl

[12] Siberian Advences in Mathematics, 15:2 (2005), 115–125 | MR | MR | Zbl

[13] Turmetov B. Kh., Torebek B. T., “Modifitsirovannye operatory Bavrina i ikh primeneniya”, Differentsialnye uravneniya, 51:2 (2015), 240–250 | DOI | MR | Zbl

[14] Berdyshev A. S., Turmetov B. Kh., Kadirkulov B. Zh., “Nekotorye svoistva i primeneniya integro-differentsialnykh operatorov tipa Adamara–Marsho v klasse garmonicheskikh funktsii”, Sibirskii matematicheskii zhurnal, 53:4 (2012), 752–764 | MR | Zbl

[15] Bitsadze A. V., Samarskii A. A., “O nekotorykh prosteishikh obobscheniyakh lineinykh ellipticheskikh zadach”, Doklady AN SSSR, 185:4 (1969), 739–740 | Zbl

[16] Ilin V. A., Moiseev E. I., “Nelokalnaya kraevaya zadacha pervogo roda dlya operatora Shturma–Liuvillya v differentsialnoi i raznostnoi traktovke”, Doklady AN SSSR, 291:3 (1986), 534–539 | MR

[17] Pulatov A. K., “Ob odnoi zadache Bitsadze–Samarskogo”, Differentsialnye uravneniya, 25:3 (1989), 537–540 | MR | Zbl

[18] F. Criado, F. Criado (Jr.), N. Odishelidze, “On the solution of some non-local problems”, Czechoslovak Mathematical Journal, 54:2 (2004), 487–498 | DOI | MR | Zbl

[19] Kishkis K. Yu., “Ob odnoi nelokalnoi zadache dlya garmonicheskikh v mnogosvyaznoi oblasti funktsii”, Differentsialnye uravneniya, 23:1 (1987), 174–177 | MR | Zbl

[20] A. S. Berdyshev, B. J. Kadirkulov, J. J. Nieto, “Solvability of an elliptic partial differential equation with boundary condition involving fractional derivatives”, Complex Variables and Elliptic Equations, 59:5 (2014), 680–692 | DOI | MR | Zbl

[21] M. A. Sadybekov, B. K. Turmetov, B. T. Torebek, Electronic Journal of Differential Equations, 2014 (2014), No. 157, 14 pp. | MR

[22] M. Kirane, B. T. Torebek, Mathematical Methods in the Applied Sciences, 2015 (to appear)

[23] Vasileva A. B., Tikhonov N. A., Integralnye uravneniya, 2-e izd., “FIZMATLIT”, M., 2002, 160 pp.

[24] Torebek B. T., Turmetov B. Kh., “K voprosu razreshimosti nekotorykh obratnykh zadach dlya uravneniya Laplasa s granichnym operatorom Rimana–Liuvillya”, Vestnik KarGU. Seriya matematika, 69:1 (2013), 113–121