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**On a problem for the third order equation with parabolic-hyperbolic operator including a fractional derivative.**
*(English)*
Zbl 1490.35231

Summary: This work devoted to one valued solvability of a local problem for a parabolic-hyperbolic type differential equation of third order involving Gerasimov-Caputo fractional operator. Boundary value problem, involving third boundary condition on the parabolic domain and discontinuous gluing condition on the line \(x=0\), is considered. The problem replaced by Volterra type nonlinear integral equations. The existence of solution is proved by the method of successive approximations of factorial law.

### Keywords:

parabolic-hyperbolic type; Gerasimov-Caputo derivatives; discontinuous gluing condition; integral equations
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\textit{O. Kh. Abdullaev} and \textit{A. A. Matchanova}, Lobachevskii J. Math. 43, No. 2, 275--283 (2022; Zbl 1490.35231)

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### References:

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