For the equation
$$xu_{xx} + yu_{yy} + \alpha u_x + \beta u_y = 0,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} < \alpha ,\beta < 1,$$
(1)
in the domain
D bounded by a Jordan curve
σ with endpoints
A(1, 0) and
B(0, 1) and the segment
OB(
x = 0, 0 ≤
y ≤ 1) for
x > 0 and
y > 0 and by the characteristics
OC:
x +
y = 0 and √
x + √?
y = 1 of Eq. (1) for
x > 0 and
y < 0, we consider a nonlocal boundary value problem with data on the curve
σ and the segment
OB and with a boundary condition containing a generalized fraction integro-differentiation operator in the characteristic domain of Eq. (1) for
x > 0 and
y < 0.
We prove the existence of a regular solution of this problem for the case in which the “normal curve”