The principal aim of the paper is to establish the function <img border=0 width=102 height=21 src="http://fbpe/img/proy/v28n1/img03.jpg" alt="http:/fbpe/img/proy/v28n1/img03.jpg">and its properties by using Fractional Calculus. We also obtained some integral representations of the function <img border=0 width=64 height=27 src="http://fbpe/img/proy/v28n1/img02.jpg" alt="http:/fbpe/img/proy/v28n1/img02.jpg">which is recently introduced by Shukla and Prajapati[6].