  In this paper, we consider a nonlocal boundary-value problem for a mixed-type
equation involving the bi-ordinal Hilfer fractional derivative in a rectangular
domain. The main target of this work is to analyze the uniqueness and the
existence of the solution of the considered problem by means of eigenfunctions.
Moreover, we construct the solution of the ordinary fractional differential
equation with the right-sided bi-ordinal Hilfer derivative by the method of
reduction to the Volterra integral equation. Then, we present sufficient
conditions for given data in order to show the existence of the solution.
