This article is cited in 1 paper

Differential Equations and Mathematical Physics

On a problem for mixed type equation with partial Riemann–Liouville fractional derivative

O. A. Repin^ab, A. V. Tarasenko<sup>b

a</sup> Samara State Economic University, Samara, 443090, Russian Federation
^b Samara State Technical University, Samara, 443100, Russian Federation

Abstract: The uniqueness and existence of solutions of a nonlocal problem proved for an equation of mixed type. This equation contains diffusion equation of fractional order. The boundary condition contains a linear combination of generalized operators of fractional order with the Gauss hypergeometric function. The solution of the problem is given explicitly.

Keywords: boundary value problem, generalized fractional integro-differentiation operator, differential equation of fractional order, Gauss hypergeometric function.

UDC: 517.956.6

MSC: 35M12

Original article submitted 25/X/2016
revision submitted – 14/XI/2016

DOI: 10.14498/vsgtu1516

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