Geodesic
Boundary value problems for a linear ordinary differential equation of fractional order with delay
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 685-695

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In this paper we obtained the explicit representations of the solutions of Dirichlet and Neumann problems for a linear ordinary differential equation of fractional order with delay. The Green's functions of the problems are constructed. The theorems of existence and uniqueness of solutions of investigated problems are proved. It is proved that the solvability conditions can be violated only a finite number of times.
Keywords: differential equation of fractional order, differential equation with delay, the generalized Mittag-Leffler function, the generalized Wright function, the Green's function. 
@article{SEMR_2018_15_a92,
     author = {M. G. Mazhgikhova},
     title = {Boundary value problems for a linear ordinary differential equation of fractional order with delay},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {685--695},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a92/}
}
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M. G. Mazhgikhova. Boundary value problems for a linear ordinary differential equation of fractional order with delay. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 685-695. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a92/