International Bulletin of Mathematical Research Volume 2, Issue 1, March 2015 Pages: 87-92, ISSN: 2394-7802 Received: February 20, 2015 Keywords: General class of functions; I-function; Mellin Barnes contour integral; N-fractional calculus. AMS Classification: 33C45, 33C47, 33E20 On N-Fractional Calculus Pertaining to I-Function Alok Bhargava 1 , Amber Srivastava 2 and Rohit Mukherjee 3 1 Department of Mathematics, Poornima University, Jaipur, Rajasthan, India Email: alokbhargava2003@yahoo.co.in 2,3 Department of Mathematics, Swami Keshvanand Institute Of Technology, Management & Gramothan, Jaipur-302017, Rajasthan, India Email: 2 prof.amber@gmail.com , 3 rohit@skit.ac.in Abstract In the present paper we establish two theorems pertaining to N-fractional calculus of product of a general class of functions and I- function. The main results provide useful extension and unification of a number of (known or new) results for various special cases of the general class of functions and I-function. For the sake of illustration, we obtain four corollaries as special cases of the main results. 1 INTRODUCTION (a) The general class of functions introduced by Kumar [12] is defined in the following form: (1.1) where (i) and are real numbers. (ii) and u are natural numbers. (iii) (iv) , z is a complex variable and is an arbitrary constant. The general class of functions defined by (1.1) is general in nature as it unifies and extends a number of useful functions such as unified Riemann-zeta function [10], hypergeometric function and generalized hypergeometric function [3,4], Bessel function and generalized Bessel function [1], Struve’s function and Lommel’s function [2], generalized Mittag–Leffler function [7,11] etc. (see, e.g. [2]). Recently, Kumar [12, 13] has also studied and discussed in detail, the convergence and N-fractional calculus of this general class of functions. (b) For the present study, we use the I-function studied by Saxena [14] and defined as: (1.2)