Russian Mathematics

, Volume 61, Issue 4, pp 35–40 | Cite as

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

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Abstract

We consider a question on unique solvability of a boundary-value problem with fractional derivatives for a mixed-type equation of second order. We prove first a uniqueness theorem. The existence theorem is proved by means of reduction to Fredholm equation of the second kind, and its unconditional solvability follows from the uniqueness of solution.

Keywords

operator of fractional differentiation Gauss hypergeometric function Cauchy problem Fredholm integral equation 

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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Samara State Economic UniversitySamaraRussia
  2. 2.Kabardino-Balkarian State UniversityNal’chikRussia

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