Hyper-Bessel functions as multi-index Mittag-Leffler functions: Relations containing generalized Erdélyi–Kober fractional integrals

Abstract

Studying the properties of the hyper-Bessel functions, integrals and derivatives of an arbitrary order of them are found. As a result, different relations between these integrals and derivatives and functions of the considered kind are obtained. An interesting relation containing generalized Erdélyi–Kober fractional integral is also obtained.