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 mixed-type equation with a regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's 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 the explicit solution of initial problems for a differential equation with the bi-ordinal Hilfer's derivative and regularized Caputo-like counterpart of the hyper-Bessel differential operator with the non-zero starting point.

18 pages

References in corpus (4)

• Determination of the order of fractional derivative for subdiffusion equation
• Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator
• Non-local boundary value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional differential operators
• Tricomi type boundary value problem with integral conjugation condition for a mixed type equation with Hilfer fractional operator