On nonlocal problem with fractional Riemann–Liouville derivatives for a mixed-type equation

The unique solvability is investigated for the problem of equation with partial fractional derivative of Riemann–Liouville and boundary condition that contains the generalized operator of fractional integro-differentiation. The uniqueness theorem for the solution of the problem is proved on the basis of the principle of optimality for a nonlocal parabolic equation and the principle of extremum for the operators of fractional differentiation in the sense of Riemann–Liouville. The proof of the existence of solutions is equivalent to the problem of solvability of differential equations of fractional order. The solution is obtained in explicit form.