Solvability of the boundary?value problem for a mixed equation involving hyper?Bessel fractional differential operator and bi?ordinal Hilfer fractional derivative

In a rectangular domain, boundary-value problem is considered for mixed-type equation with regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's fractional derivative. Using method separation variables, Laplace transform, unique solvability has been established. Moreover, we have found explicit solution initial problems derivative non-zero starting point.