Investigation of solution of Riemann boundary value problem on ray with infinite index with new method

In this paper we consider the Riemann boundary value problem with an infinite fractional index exceeding half and less than one when the boundary condition for the desired analytic function is given on the positive real axis of the complex plane. To solve the problem, the approach based on eliminating an infinite discontinuity of the argument of the coefficient of the boundary condition using a specially selected analytic function representing an exponential function with the fractional power of the argument is used.