Inside boundary value problem for mixed type equation of the third order with multiple characteristics

We investigated a boundary value problem with operator fractional differentiation in boundary conditions for mixed type equation of the third order. At restrictions of inequality type on the known functions and different order fractional differentiation operator in boundary condition the uniqueness theorem is proved. Existence of the solution is proved by way to reductions to second sort equation of Fredgolm, unconditional solubility of which follows from uniqueness of the solution of the problem.