This article is cited in 3 papers

Nonlocal problem with fractional derivatives for mixed type equation

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, Kabardino-Balkarian State University, 173 Chernyshevskii str., Nalchik, 360004 Russia

Abstract: The paper is devoted to the study of a boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in boundary conditions. Under restrictions inequality type on the known functions and different orders of generalized fractional differentiation operators in boundary conditions we prove the theorem of uniqueness. Existence of the solution is proved by the reductions to equation of Fredholm second sort, which unconditional solvability follows from uniqueness of the solution of the problem.

Keywords: a boundary-value problem, regular solution, operator of fractional integration, operator of fractional differentiation, Fredholm's and Abel's integral equations of the second type, singular integral equation with Cauchy kernel, regularization.

UDC: 517.956

Received: 14.02.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:8, 65–70

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