On a new (p,q)-Mathieu-type power series and its applications

Abstract

Our aim in this paper, is to establish certain new integral representations for the (p,q)-Mathieu-type power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of these special function. Moreover, we introduce the notion of the (p, q)-Mittag- Leffler functions and we present a relationships between these two functions. Some other applications are proved, in particular two Tur?n type inequalities for the (p,q)-Mathieu-type series are derived.