On a time-nonlocal boundary value problem for time-fractional partial differential equation

A boundary value problem with a nonlocal m-point condition in time for a space-degenerate partial differential equation involving the bi-ordinal Hilfer fractional derivative is the main subject of the present investigation.We aim to prove a unique solvability of this problem based on certain properties of the Legendre polynomials and the two-parameter Mittag-Leffler function.An explicit solution to the considered problem is found in the form of the Fourier-Legendre series.