Non-local boundary value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional differential operators

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.