Geodesic
The Dirichlet Problem for a mixed-type equation with fractional derivatives
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2022), pp. 83-94

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In this paper we study the first boundary value problem for equation of mixed type with fractional derivatives in a rectangular domain. The criterion for the uniqueness of the solution of the problem is established. The solution is constructed as a sum of an orthogonal series and its convergence is shown in the class of regular solutions of this equations. The stability of the solution with respect to given boundary functions is established in the class of continuous and square-summable functions.
Keywords: the mixed-type equation with fractional derivatives, the Dirichlet problem, criterion of uniqueness, series, stability.
Mots-clés : existence 
@article{IVM_2022_9_a7,
     author = {K. B. Sabitov},
     title = {The {Dirichlet} {Problem} for a mixed-type equation with fractional derivatives},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--94},
     publisher = {mathdoc},
     number = {9},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_9_a7/}
}
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K. B. Sabitov. The Dirichlet Problem for a mixed-type equation with fractional derivatives. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2022), pp. 83-94. http://geodesic.mathdoc.fr/item/IVM_2022_9_a7/