On a problem with a displacement for a partial differential equation

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 integrodifferentiation
• gauss hypergeometric function
• fredholm equation of the second kind