On a boundary-value problem with Saigo operators for a mixed-type equation

The theory of mixed type equations is one of the most important parts of the theory of partial differential equations. This is due to the fact that equations of mixed type are connected with the problems of the theory of singular integral equations, integral transformations, and special functions. An actual continuation of the research in these fields will be the proof of the unique solvability of the inner-boundary problem. In the hyperbolic part of the domain, a condition is established that relates the generalized derivatives and fractional-order integrals to the Gauss hypergeometric function.

boundary value problem, Gauss hypergeometric function, fractionalorder operator, Cauchy problem, integral equations