Geodesic
The Cauchy and Dirichlet problems for ordinary differential equation of second order with regularized derivative of segment order
News of the Kabardin-Balkar scientific center of RAS, no. 2 (2016), pp. 30-34.

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

For an ordinary differential equation of second order with regularized derivative of segment order we build a fundamental solution, that is used to provide explicit solution for the Cauchy and Dirichlet problems.
Keywords: regularized derivative of segment order, regularized fractional derivative, Cauchy problem, Dirichlet problem. 
@article{IZKAB_2016_2_a5,
     author = {B. I. Efendiev},
     title = {The {Cauchy} and {Dirichlet} problems for ordinary differential equation of second order with regularized derivative of segment order},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {30--34},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IZKAB_2016_2_a5/}
}
TY  - JOUR
AU  - B. I. Efendiev
TI  - The Cauchy and Dirichlet problems for ordinary differential equation of second order with regularized derivative of segment order
JO  - News of the Kabardin-Balkar scientific center of RAS
PY  - 2016
SP  - 30
EP  - 34
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IZKAB_2016_2_a5/
LA  - ru
ID  - IZKAB_2016_2_a5
ER  - 
%0 Journal Article
%A B. I. Efendiev
%T The Cauchy and Dirichlet problems for ordinary differential equation of second order with regularized derivative of segment order
%J News of the Kabardin-Balkar scientific center of RAS
%D 2016
%P 30-34
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IZKAB_2016_2_a5/
%G ru
%F IZKAB_2016_2_a5
B. I. Efendiev. The Cauchy and Dirichlet problems for ordinary differential equation of second order with regularized derivative of segment order. News of the Kabardin-Balkar scientific center of RAS, no. 2 (2016), pp. 30-34. http://geodesic.mathdoc.fr/item/IZKAB_2016_2_a5/

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

[2] A. V. Pskhu, “K teorii operatora integro-differentsirovaniya kontinualnogo poryadka”, Differents. uravneniya, 40:1 (2004), 120–127 | MR | Zbl

[3] A. V. Sokhieva, “Analog formuly Nyutona-Leibnitsa dlya regulyarizovannogo operatora differentsirovaniya kontinualnogo poryadka”, Dokl. Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 8:1 (2005), 84–86

[4] B. I. Efendiev, “Zadacha Koshi dlya obyknovennogo differentsialnogo uravneniya vtorogo poryadka s kontinualnoi proizvodnoi”, Differents. uravneniya, 47:9 (2011), 1364–1368 | MR | Zbl

[5] B. I. Efendiev, “Zadacha Dirikhle dlya obyknovennogo differentsialnogo uravneniya vtorogo poryadka s kontinualnoi proizvodnoi”, Mat. zametki, 97:4 (2015), 620–628

[6] B. I. Efendiev, “Zadacha Steklova dlya obyknovennogo differentsialnogo uravneniya vtorogo poryadka s kontinualnoi proizvodnoi”, Differents. uravneniya, 49:4 (2013), 469–475 | Zbl

[7] B. I. Efendiev, “Nachalnaya zadacha dlya nepreryvnogo differentsialnogo uravneniya vtorogo poryadka”, Differents. uravneniya, 50:4 (2014), 564–568 | Zbl