O. A. Repin, S. K. Kumykova, “Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 4(25),Pages <nobr>25

This article is cited in 13 papers

Differential Equations

Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order

O. A. Repin^a, S. K. Kumykova^b

^a Dept. of Mathematical Statistics and Econometrics, Samara State Economic University, Samara
^b Dept. of Function Theory, Kabardino-Balkar State University, Nal'chik

Abstract: The unique solvability of internally boundary value problem for equation of mixed type of third order with multiple characteristics is investigated. The uniqueness theorem is proved with the restrictions on certain features and different orders of fractional integro-differentiation. The existence of solution is equivalent reduced to a Fredholm integral equation of the second kind.

Keywords: boundary value problem, fractional integro-differentiation operators, Gauss hypergeometric function, Fredholm integral equation.

UDC: 517.956.6 + 517.968.23

MSC: Primary 35M12; Secondary 26A33, 33C05

Original article submitted 17/X/2011
revision submitted – 23/XI/2011

DOI: 10.14498/vsgtu1014