Geodesic
Boundary value problem with shift for a fractional order delay differential equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 28 (2019) no. 3, pp. 16-25

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In this paper we prove existence and uniqueness theorem to a boundary value problem with shift for a fractional order ordinary delay differential equation. The solution of the problem is written out in terms of the Green function. We find an explicit representation for solvability condition and show that it may only be violated a finite number of times.
Keywords: Green function, delay differential equation, fractional differential equation, generalized Mittag-Leffler function, generalized Wright function. 
@article{VKAM_2019_28_3_a1,
     author = {M. G. Mazhgikhova},
     title = {Boundary value problem with shift for a fractional order delay differential equation},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {16--25},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2019_28_3_a1/}
}
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M. G. Mazhgikhova. Boundary value problem with shift for a fractional order delay differential equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 28 (2019) no. 3, pp. 16-25. http://geodesic.mathdoc.fr/item/VKAM_2019_28_3_a1/