Geodesic
Cauchy problem for ordinary differential equation with Riemann-Liouville operator with delay
News of the Kabardin-Balkar scientific center of RAS, no. 1 (2017), pp. 24-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Cauchy problem for differential equations of fractional order with delay had been studied. The theorem of existence and uniqueness of solution of the problem is proved.
Keywords: Cauchy problem, the differential equation of fractional order, Riemann-Liouville operator, differential equation with delay. 
@article{IZKAB_2017_1_a3,
     author = {M. G. Mazhgikhova},
     title = {Cauchy problem for ordinary differential equation with {Riemann-Liouville} operator with delay},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {24--28},
     year = {2017},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IZKAB_2017_1_a3/}
}
TY  - JOUR
AU  - M. G. Mazhgikhova
TI  - Cauchy problem for ordinary differential equation with Riemann-Liouville operator with delay
JO  - News of the Kabardin-Balkar scientific center of RAS
PY  - 2017
SP  - 24
EP  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IZKAB_2017_1_a3/
LA  - ru
ID  - IZKAB_2017_1_a3
ER  - 
%0 Journal Article
%A M. G. Mazhgikhova
%T Cauchy problem for ordinary differential equation with Riemann-Liouville operator with delay
%J News of the Kabardin-Balkar scientific center of RAS
%D 2017
%P 24-28
%N 1
%U http://geodesic.mathdoc.fr/item/IZKAB_2017_1_a3/
%G ru
%F IZKAB_2017_1_a3
M. G. Mazhgikhova. Cauchy problem for ordinary differential equation with Riemann-Liouville operator with delay. News of the Kabardin-Balkar scientific center of RAS, no. 1 (2017), pp. 24-28. http://geodesic.mathdoc.fr/item/IZKAB_2017_1_a3/

[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] Мир, М., 1967

[6] A. D. Myshkis, Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972 | MR

[7] L. E. Elsgolts, S. B. Norkin, Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M., 1971

[8] Мир, М., 1984

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

[10] A. N. Zarubin, “Nachalno-kraevaya zadacha dlya uravneniya smeshannogo tipa s zapazdyvayuschim argumentom”, Differents. Uravneniya, 34:1 (1998), 87–93 | MR | Zbl

[11] A. N. Zarubin, “Ob algoritme resheniya nachalno-kraevoi zadachi dlya uravneniya smeshannogo tipa s zapazdyvayuschim argumentom”, Zh. vychisl. matem. i matem. fiz, 37:2 (1997), 184–187 | MR | Zbl

[12] 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

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

[14] M. G. Mazhgikhova, “Zadacha Neimana dlya obyknovennogo differentsialnogo uravneniya drobnogo poryadka s zapazdyvayuschim argumentom”, Izvestiya KBNTs RAN, 2016, no. 2 (70), 15–20

[15] M. G. Mazhgikhova, “Nachalnaya zadacha dlya obyknovennogo differentsialnogo uravneniya s proizvodnoi Rimana-Liuvillya s zapazdyvayuschim argumentom”, Uchenye zapiski Orlovskogo gosudarstvennogo universiteta, 2015, no. 4 (67), 46–47

[16] 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

[17] 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

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

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