This article is cited in 4 papers

Solvability of a nonlocal problem for a loaded parabolic-hyperbolic equation

A. V. Tarasenko

Chair of Higher Mathematics, Samara State University of Architecture and Building, Samara, Russia

Abstract: For a mixed-type equation we study a problem with generalized fractional integro-differentiation operators in the boundary condition. We prove its unique solvability under inequality-type conditions imposed on the known functions for various orders of fractional integro-differentiation operators. We prove the existence of a solution to the problem by reducing the latter to a fractional differential equation.

Keywords: boundary value problem, generalized fractional integro-differentiation operators, Gauss hypergeometric function.

UDC: 517.956

Received: 15.12.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:1, 64–71

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