Geodesic
Solvability of a~nonlocal problem for a~loaded parabolic-hyperbolic equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2013), pp. 73-81

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For a mixed-type equation we study a problem with generalized fractional integro-differentiation operators in the boundary condition. We prove its unique solvability under inequality-type conditions imposed on the known functions for various orders of fractional integro-differentiation operators. We prove the existence of a solution to the problem by reducing the latter to a fractional differential equation.
Keywords: boundary value problem, generalized fractional integro-differentiation operators, Gauss hypergeometric function. 
@article{IVM_2013_1_a6,
     author = {A. V. Tarasenko},
     title = {Solvability of a~nonlocal problem for a~loaded parabolic-hyperbolic equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {73--81},
     publisher = {mathdoc},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_1_a6/}
}
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A. V. Tarasenko. Solvability of a~nonlocal problem for a~loaded parabolic-hyperbolic equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2013), pp. 73-81. http://geodesic.mathdoc.fr/item/IVM_2013_1_a6/