24 research outputs found
First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
In this work, we obtain the first and second fundamental
solutions (FS) of the multidimensional time-fractional equation with
Laplace or Dirac operators, where the two time-fractional derivatives
of orders α ∈]0, 1] and β ∈]1, 2] are in the Caputo sense. We obtain
representations of the FS in terms of Hankel transform, double Mellin-
Barnes integrals, and H-functions of two variables. As an application,
the FS are used to solve Cauchy problems of Laplace and Dirac type
One-Dimensional and Multi-Dimensional Integral Transforms of Buschman–Erdélyi Type with Legendre Functions in Kernels
This paper consists of two parts. In the first part we give a brief survey of results on Buschman–Erdélyi operators, which are transmutations for the Bessel singular operator. Main properties and applications of Buschman–Erdélyi operators are outlined. In the second part of the paper we consider multi-dimensional integral transforms of Buschman–Erdélyi type with Legendre functions in kernels. Complete proofs are given in this part, main tools are based on Mellin transform properties and usage of Fox H-functions