This article is cited in 9 papers

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

On the problem with generalized operators of fractional differentiation for mixed type equation with two degeneracy lines

O. A. Repin^ab, S. K. Kumykova<sup>c

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

Abstract: The nonlocal problem for mixed-type equation with perpendicular lines of degeneracy is investigated for the case when the Dirichlet condition is given on the elliptic boundary, and the generalized derivatives of the solution values on the characteristics are pointwise related to the solution and its normal derivatives values on the lines of a parabolic degeneracy in its hyperbolic parts.

Keywords: nonlocal problem, regular solution, operators of fractional integro-differentiation, Cauchy problem, Fredholm equation, singular integral equation with Cauchy kernel, regularizer, Abel equation.

UDC: 517.956.6

MSC: Primary 35M10; Secondary 26A33, 35A05

Original article submitted 22/X/2012
revision submitted – 16/XI/2012

DOI: 10.14498/vsgtu1141

Bibliographic databases:

• 
• 
•