This article is cited in 3 papers

Nonlocal problem with generalized operators of fractional differentiation for an equation of mixed type in an unbounded domain

O. A. Repin^a, S. K. Kumykova<sup>b

a</sup> Chair of Mathematical Statistics and Econometrics, Samara State Economic University, 141 Sovetskoi Armii str., Samara, 443090 Russia
^b Chair of Function Theory and Functional Analysis, Kabardino-Balkarian State University, 173 Chernyshevskogo str., Nal'chik, 360004 Russia

Abstract: For mixed-type equation we study the problem with generalized operators of fractional differentiation whose kernels contain the Gauss hypergeometric functions. Under restrictions in the form of inequalities on known functions and various parameters of operators we prove the unique solvability of the posed boundary-value problem.

Keywords: Riemann–Liouville integral and derivative of fractional order, singular integral equation, Fredholm equation, Gauss hypergeometric function.

UDC: 517.946

Received: 14.02.2013
Revised: 05.11.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:4, 50–53

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