A nonlocal boundary value problem for a mixed type equation

In the present paper, in a certain finite mixed domain for the equation (signy)jyjmuxx + uyy + α0 jyj1− m2 ux + βy0uy = 0 we study the problem with a nonlocal condition pointwise connecting the value of the unknown function on the boundary and parallel to it internal characteristic, using the fractional order differentiation operator in the sense of Riemann-Liouville. On the segment of the degeneration line, a general conjugation condition and an analogue of the Frankl condition type are specified. The uniqueness of the solution to the problem is proved using the extremum principle of A.V. Bitsadze. The existence of a solution to the problem is proved using the theory of singular integral equations, Wiener-Hopf equations and Fredholm equations of the second kind.