The solution of Tricomi problem for the mixed type equation with Bessel operator with the method of the theory of the integral equations

In this article the existence and uniqueness of Tricomi problem solution is proven for Lavrentiev–Bizadze equation with the Bessel operator:
$$ x^{-k}\frac\partial{\partial x}\biggl(x^k\frac{\partial u}{\partial x}\biggr)+\operatorname{sign}y\frac{\partial^2u}{\partial y^2}=0 $$
in $D$ area limited with the rectifiable $\Gamma$ curve, $Oy$ axis and $OC\colon x+y=0$ and $BC\colon x-y=1$ characteristics, by method of the integral equations.