Geodesic
Green's function of an interior boundary-value problem for a fractional ordinary differential equation with constant coefficients
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 25-34

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We consider an interior boundary-value problem for a linear, ordinary differential equation with an operator of fractional, discretely distributed differentiation. The boundary conditions connect the values of the unknown solution at the ends of the interval with the values at interior points. Green's function is constructed and the theorem of the existence and uniqueness of a solution is proved.
Keywords: interior boundary value problem, Green's function, Caputo derivative, fractional ordinary differential equation, operator of discretely distributed differentiation. 
@article{INTO_2021_195_a2,
     author = {L. Kh. Gadzova},
     title = {Green's function of an interior boundary-value problem for a fractional ordinary differential equation with constant coefficients},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {25--34},
     publisher = {mathdoc},
     volume = {195},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_195_a2/}
}
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L. Kh. Gadzova. Green's function of an interior boundary-value problem for a fractional ordinary differential equation with constant coefficients. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 25-34. http://geodesic.mathdoc.fr/item/INTO_2021_195_a2/