This article is cited in 1 paper

Differential Equations and Mathematical Physics

An internal boundary value problem with the Riemann–Liouville operator for the mixed type equation of the third order

O. A. Repin^ab, S. K. Kumykova<sup>c

a</sup> Samara State Technical University, Samara, 443100, Russian Federation
^b Samara State University of Economics, Samara, 443090, Russian Federation
^c Kabardino-Balkar State University, Nalchik, 360004, Russia

Abstract: The unique solvability of the internal boundary value problem is investigated for the mixed type equation of the third order with Riemann–Liouville operators in boundary condition. The uniqueness theorem is proved for the different orders of operators of fractional integro-differentiation when the inequality constraints on the known functions exist. The existence of solution is verified by the method of reduction to Fredholm equations of the second kind, which unconditional solvability follows from the uniqueness of the solution of the problem.

Keywords: mixed type equation, Fredholm equation, Cauchy problem, fractional operators in the sense of Riemann–Liouville integro-differentiation.

UDC: 517.956.6

MSC: 35M12

Original article submitted 21/XI/2015
revision submitted – 13/II/2016

DOI: 10.14498/vsgtu1461

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