This article is cited in 3 papers

On solvability of nonlocal problem for loaded parabolic-hyperbolic equation

A. V. Tarasenko

Samara State Architecture and Civil Engineering University, 194 Molodogvardeiskaya str., Samara, 443001 Russia

Abstract: We study unique solvability of a nonlocal problem for equations of mixed type in a finite domain. This equation contains partial fractional Riemann–Liouville derivative. The boundary condition of the problem contains a linear combination of operators of fractional differentiation in the sense of Riemann–Liouville and generalized operators of fractional integro-differentiation in the sense of M. Saigo. The uniqueness theorem of the problem is proved by a modified Tricomi method. The existence of solutions is equivalently reduced to the solvability of Fredholm integral equation of the second kind.

Keywords: boundary-value problem, equation of mixed type, operators of fractional integro-differentiation in the Riemann–Liouville sense, generalized operators of fractional integro-differentiation in the M. Saigo sense, Fredholm integral equation of the second kind.

UDC: 517.956

Received: 11.01.2017

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:3, 53–59

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