On a problem with a displacement for a partial differential equation.

*(Russian. English summary)*Zbl 1413.35344Summary: The unique solvability of the problem with the generalized operators of fractional integro-differentiation in the boundary condition is investigated for the mixed type equation. The uniqueness theorem for the nonlocal problem is proved. The proof of existence of the problem solution is reduced to the demonstration of solvability of Fredholm integral equation of the second kind.

##### MSC:

35M12 | Boundary value problems for PDEs of mixed type |

35M10 | PDEs of mixed type |

35R11 | Fractional partial differential equations |

35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |

##### Keywords:

boundary value problem; generalized operator of fractional integro-differentiation; Gauss hypergeometric function; Fredholm equation of the second kind
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\textit{A. V. Tarasenko}, Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 2013, No. 3(32), 21--28 (2013; Zbl 1413.35344)

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##### References:

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