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