On some generalizations of the properties of the multidimensional generalized Erdélyi-Kober operators and their applications

In this paper we investigate the composition of a multidimensional generalized Erdélyi-Kober operator with differential operators of high order. In particular, with powers of the differential Bessel operator. Applications of proved properties to solving the Cauchy problem for a multidimensional polycaloric equation with a Bessel operator are show

Some recent developments in the transmutation operator approach

This is a brief overviewof some recent developments in the transmutation operator approach to practical solution of mathematical physics problems. It introduces basic notions and results of transmutation theory, and gives a brief historical survey with some important references. Mainly applications to linear ordinary and partial differential equations and to related boundary value and spectral problems are discusse