Geodesic
An estimate for the first eigenvalue of the Dirichlet problem for an ordinary differential equation with fractional derivatives with different origins
News of the Kabardin-Balkar scientific center of RAS, no. 1 (2017), pp. 34-40.

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

We study the Dirichlet problem for an ordinary linear differential equation of fractional order. The principal differential part of the equation is the composition of Riemann-Liouville and Caputo fractional derivatives with the different origins. In the paper, we found a lower-bound estimate for the first eigenvalue of the problem.
Keywords: fractional derivative, Riemann-Liouville derivative, Caputo derivative, Dirichlet problem, eigenvalue. 
@article{IZKAB_2017_1_a5,
     author = {Eneyeva L. M.},
     title = {An estimate for the first eigenvalue of the {Dirichlet} problem for an ordinary differential equation with fractional derivatives with different origins},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {34--40},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IZKAB_2017_1_a5/}
}
TY  - JOUR
AU  - Eneyeva L. M.
TI  - An estimate for the first eigenvalue of the Dirichlet problem for an ordinary differential equation with fractional derivatives with different origins
JO  - News of the Kabardin-Balkar scientific center of RAS
PY  - 2017
SP  - 34
EP  - 40
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IZKAB_2017_1_a5/
LA  - ru
ID  - IZKAB_2017_1_a5
ER  - 
%0 Journal Article
%A Eneyeva L. M.
%T An estimate for the first eigenvalue of the Dirichlet problem for an ordinary differential equation with fractional derivatives with different origins
%J News of the Kabardin-Balkar scientific center of RAS
%D 2017
%P 34-40
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IZKAB_2017_1_a5/
%G ru
%F IZKAB_2017_1_a5
Eneyeva L. M. An estimate for the first eigenvalue of the Dirichlet problem for an ordinary differential equation with fractional derivatives with different origins. News of the Kabardin-Balkar scientific center of RAS, no. 1 (2017), pp. 34-40. http://geodesic.mathdoc.fr/item/IZKAB_2017_1_a5/

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

[2] S. Sh. Rekhviashvili, “K opredeleniyu fizicheskogo smysla drobnogo integrodifferentsirovaniya”, Nelineinyi mir, 5:4 (2007), 194–197

[3] S. Sh. Rekhviashvili, “Formalizm Lagranzha s drobnoi proizvodnoi v zadachakh mekhaniki”, Pisma v ZhTF, 30:2 (2004), 33–37

[4] B. Stanković, “An equation with left and right fractional derivatives”, Publications de l'institute mathématique, Nouvelle série, 2006, no. 80 (94), 259–272 | DOI | MR | Zbl

[5] T. M. Atanacković, B. Stanković, “On a differential equation with left and right fractional derivatives”, Fractional calculus and applied analysis, 10:2 (2007), 139–150 | MR | Zbl

[6] L. M. Eneeva, “Kraevaya zadacha dlya differentsialnogo uravneniya s proizvodnymi drobnogo poryadka s razlichnymi nachalami”, Vestnik KRAUNTs. Fiz. mat. nauki, 2015, no. 2 (11), 39–44 | Zbl