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.

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

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},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     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
PB  - mathdoc
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
%I mathdoc
%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.