Investigation of the solution of a half-order elliptic type equation with non-local boundary condition

Abstract The article is devoted to the investigation of the solution structure of an elliptic-type equation containing a half-order operator derived through the factorization of the Cauchy–Riemann equation defined in the rectangle region. Under fulfillment of the Carleman’s condition on the boundary of the rectangle region where the equation is set, the solution is constructed in explicit form. The most important result emerges from the study that a solution for the problem in the form of a Mittag–Leffler is found for the first time.