The problem with Saigo operators for a hyperbolic equation that degenerates inside the domain

Abstract

A nonlocal problem is investigated for a degenerate hyperbolic equation $$ |y|^{m} u_{xx}-u_{yy}+a |y|^{\frac{m}{2}-1} u_{x}=0 $$ in a domain bounded by the characteristics of this equation. The boundary condition for this problem contains a linear combination of generalized fractional integro-differentiation operators with a hypergeometric Gauss function in the kernel. The uniqueness of the solution is proved using the Tricomi method. The existence of a solution is equivalent to the solvability of a singular integral equation with a Cauchy kernel.

Keywords

• boundary value problem
• fractional integro-differentiation operators
• gauss function
• singular integral equation