Geodesic
Boundary-value problem with Saigo operators for mixed type equation of the third order with multiple characteristics
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 49-57

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We study a boundary-value problem with shift for mixed-type equation of the third order. In the hyperbolic field boundary condition contains a linear combination of generalized operators of fractional integro-differentiation. We prove a unique solvability of the problem.
Keywords: boundary-value problem, generalized operators of fractional integro-differentiation, Gauss hypergeometric function, Abel integral equation, Fredholm integral equation of the second kind. 
@article{IVM_2015_7_a4,
     author = {O. A. Repin and S. K. Kumykova},
     title = {Boundary-value problem with {Saigo} operators for mixed type equation of the third order with multiple characteristics},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {49--57},
     publisher = {mathdoc},
     number = {7},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_7_a4/}
}
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O. A. Repin; S. K. Kumykova. Boundary-value problem with Saigo operators for mixed type equation of the third order with multiple characteristics. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 49-57. http://geodesic.mathdoc.fr/item/IVM_2015_7_a4/