Geodesic
Naimark Problem for a Fractional Ordinary Differential Equation
Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 195-202

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

For a fractional ordinary differential equation, we consider a problem where the boundary conditions are given in the form of linear functionals. This permits covering a fairly broad class of linear local and nonlocal conditions. The fractional derivative is understood in the sense of Gerasimov–Caputo. A necessary and sufficient condition for the unique solvability of the problem is obtained. A representation of the solution via special functions is found. A theorem on the existence and uniqueness of the solution is proved.
Keywords: Gerasimov–Caputo fractional derivative, Naimark problem, fractional derivative, fractional equation, functional, Mittag-Leffler function. 
@article{MZM_2023_114_2_a2,
     author = {L. Kh. Gadzova},
     title = {Naimark {Problem} for a {Fractional} {Ordinary} {Differential} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {195--202},
     publisher = {mathdoc},
     volume = {114},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a2/}
}
TY  - JOUR
AU  - L. Kh. Gadzova
TI  - Naimark Problem for a Fractional Ordinary Differential Equation
JO  - Matematičeskie zametki
PY  - 2023
SP  - 195
EP  - 202
VL  - 114
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a2/
LA  - ru
ID  - MZM_2023_114_2_a2
ER  - 
%0 Journal Article
%A L. Kh. Gadzova
%T Naimark Problem for a Fractional Ordinary Differential Equation
%J Matematičeskie zametki
%D 2023
%P 195-202
%V 114
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a2/
%G ru
%F MZM_2023_114_2_a2
L. Kh. Gadzova. Naimark Problem for a Fractional Ordinary Differential Equation. Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 195-202. http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a2/