Geodesic
Nonlocal problem with generalized operators of fractional differentiation for an equation of mixed type in an unbounded domain
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2015), pp. 60-64

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For mixed-type equation we study the problem with generalized operators of fractional differentiation whose kernels contain the Gauss hypergeometric functions. Under restrictions in the form of inequalities on known functions and various parameters of operators we prove the unique solvability of the posed boundary-value problem.
Keywords: Riemann–Liouville integral and derivative of fractional order, singular integral equation, Fredholm equation, Gauss hypergeometric function. 
@article{IVM_2015_4_a6,
     author = {O. A. Repin and S. K. Kumykova},
     title = {Nonlocal problem with generalized operators of fractional differentiation for an equation of mixed type in an unbounded domain},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--64},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_4_a6/}
}
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O. A. Repin; S. K. Kumykova. Nonlocal problem with generalized operators of fractional differentiation for an equation of mixed type in an unbounded domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2015), pp. 60-64. http://geodesic.mathdoc.fr/item/IVM_2015_4_a6/