Differential Equations

On a problem with a displacement for a partial differential equation

A. V. Tarasenko

Samara State Technical University, Samara, 443100, Russia

Abstract: The unique solvability of the problem with the generalized operators of fractional integro-differentiation in the boundary condition is investigated for the mixed type equation. The uniqueness theorem for the nonlocal problem is proved. The proof of existence of the problem solution is reduced to the demonstration of solvability of Fredholm integral equation of the second kind.

Keywords: boundary value problem, generalized operator of fractional integro-differentiation, Gauss hypergeometric function, Fredholm equation of the second kind.

UDC: 517.956.6

MSC: Primary 35М12; Secondary 35M10, 35R11, 35A02

Original article submitted 14/VI/2013
revision submitted – 24/VIII/2013

DOI: 10.14498/vsgtu1255

Bibliographic databases:

• 
• 
• 
•