A boundary-value problem for a mixed type equation involving hyper-Bessel fractional differential operator and Hilfer's bi-ordinal fractional derivative

Abstract

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