This article is cited in 1 paper

The problem with operators of fractional differentiation in boundary condition for mixed-type equation

O. A. Repin^a, S. K. Kumykova<sup>b

a</sup> Samara State Economic University, 141 Sovetskoi Armii str., Samara, 443090 Russia
^b Kabardino-Balkarian State University, 173 Chernyshevskogo str., Nal'chik, 360004 Russia

Abstract: We study a question of unique solvability of a boundary-value problem with fractional derivatives for a mixed-type equation of the second order. The uniqueness theorem is proved by using restrictions on known functions. The existence of a solution to the problem is proved by reduction to the Fredholm equation of the second kind. Unconditional solvability of this equation follows from the uniqueness of a solution.

Keywords: operator of fractional differentiation, Gauss hypergeometric function, Cauchy problem, Fredholm integral equation.

UDC: 517.946

Received: 26.09.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:4, 35–40

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