Geodesic
Neumann problem for ordinary differential equation of fractional order with delay argument
News of the Kabardin-Balkar scientific center of RAS, no. 2 (2016), pp. 15-20.

Voir la notice de l'article provenant de la source Math-Net.Ru

The solution of the Neumann problem for differential equation of fractional order with delay argument has been studied. Green's function of this is constructed. The theorem of existence and uniqueness of solution of the problem is proved. A condition for unique solvability has been found.
Keywords: Neumann problem, differential equation of fractional order, differential equation with delay, the Green's function. 
@article{IZKAB_2016_2_a2,
     author = {M. G. Mazhgikhova},
     title = {Neumann problem for ordinary differential equation of fractional order with delay argument},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {15--20},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IZKAB_2016_2_a2/}
}
TY  - JOUR
AU  - M. G. Mazhgikhova
TI  - Neumann problem for ordinary differential equation of fractional order with delay argument
JO  - News of the Kabardin-Balkar scientific center of RAS
PY  - 2016
SP  - 15
EP  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IZKAB_2016_2_a2/
LA  - ru
ID  - IZKAB_2016_2_a2
ER  - 
%0 Journal Article
%A M. G. Mazhgikhova
%T Neumann problem for ordinary differential equation of fractional order with delay argument
%J News of the Kabardin-Balkar scientific center of RAS
%D 2016
%P 15-20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IZKAB_2016_2_a2/
%G ru
%F IZKAB_2016_2_a2
M. G. Mazhgikhova. Neumann problem for ordinary differential equation of fractional order with delay argument. News of the Kabardin-Balkar scientific center of RAS, no. 2 (2016), pp. 15-20. http://geodesic.mathdoc.fr/item/IZKAB_2016_2_a2/

[1] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp.

[2] J. H. Barrett, “Differential equation of non-integer order”, Canad. J. Math, 6:4 (1954), 529–541 | DOI | MR | Zbl

[3] M. M. Dzhrbashyan, A. B. Nersesyan, “Drobnye proizvodnye i zadachi Koshi dlya differentsialnykh uravnenii drobnogo poryadka”, Izv. AN ArmSSR. Matem., 1968, 3–28

[4] A. V. Pskhu, “Nachalnaya zadacha dlya lineinogo obyknovennogo differentsialnogo uravneniya drobnogo poryadka”, Mat. sbornik, 202:4 (2011), 111–122 | MR | Zbl

[5] S. B. Norkin, “O resheniyakh lineinogo odnorodnogo differentsialnogo uravneniya vtorogo poryadka s zapazdyvayuschim argumentom”, UMN, 14:1(85) (1959), 199–206 | MR | Zbl

[6] M. G. Mazhgikhova, “Nachalnaya zadacha dlya obyknovennogo differentsialnogo uravneniya drobnogo poryadka s zapazdyvayuschim argumentom”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 16:4 (2014), 28–30

[7] M. G. Mazhgikhova, “Zadacha Dirikhle dlya obyknovennogo differentsialnogo uravneneniya drobnogo poryadka s zapazdyvayuschim argumentom”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 17:2 (2015), 42–47

[8] L. Kh. Gadzova, “Zadacha Dirikhle i Neimana dlya obyknovennogo differentsialnogo uravneniya drobnogo poryadka s postoyannymi koeffitsientami”, Differentsialnye uravneniya, 51:12 (2015), 1580–1586 | MR | Zbl

[9] T. R. Prabhakar, “A singular integral equation with a generalized Mittag-Leffler function in the kernel”, Yokohama Math. J., 19 (1971), 7–15 | MR | Zbl

[10] M. M. Dzhrbashyan, Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966, 672 pp.

[11] A. K. Shukla, J. C. Prajapati, “On a generalization of Mittag-Leffler function and its properties”, J. Math. Anal. Appl., 336 (2007), 797–811 | DOI | MR | Zbl

[12] A. V. Pskhu, Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005, 199 pp.