Geodesic
The problem with operators of fractional differentiation in boundary condition for mixed-type equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2017), pp. 43-49

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We study a question of unique solvability of a boundary-value problem with fractional derivatives for a mixed-type equation of the second order. The uniqueness theorem is proved by using restrictions on known functions. The existence of a solution to the problem is proved by reduction to the Fredholm equation of the second kind. Unconditional solvability of this equation follows from the uniqueness of a solution.
Keywords: operator of fractional differentiation, Gauss hypergeometric function, Cauchy problem, Fredholm integral equation. 
@article{IVM_2017_4_a5,
     author = {O. A. Repin and S. K. Kumykova},
     title = {The problem with operators of fractional differentiation in boundary condition for mixed-type equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {43--49},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_4_a5/}
}
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O. A. Repin; S. K. Kumykova. The problem with operators of fractional differentiation in boundary condition for mixed-type equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2017), pp. 43-49. http://geodesic.mathdoc.fr/item/IVM_2017_4_a5/