Gen. Math. Notes, Vol. 7, No. 1, November 2011, pp. 33-40 ISSN 2219-7184; Copyright © ICSRS Publication, 2011 www.i-csrs.org Available free online at http://www.geman.in Application of Fractional Calculus Operators to Related Areas Kishan Sharma Department of Mathematics, NRI Institute of Technology and Management, Baraghata, Next to S.G. Motors, Jhansi Road, Gwalior-474001, India Address: B-3, Krishna Puri, Taraganj, Lashkar, Gwalior (M.P.)-474001, India E-mail: drkishan010770@yahoo.com (Received: 16-7-11/ Accepted: 14-10-11) Abstract In this paper a new function called as K-function, which is an extension of the generalization of the Mittag-Leffler function[10,11] and its generalized form introduced by Prabhakar[20], is introduced and studied by the author in terms of some special functions and derived the relations that exists between the K- function and the operators of Riemann-Liouville fractional integrals and derivatives. Keywords: Fractional calculus, Riemann- Liouville fractional integrals and derivatives. 1 Introduction Fractional Calculus is a field of applied mathematics that deals with derivatives and integrals of arbitrary orders. During the last three decades Fractional Calculus has been applied to almost every field of Mathematics like Special Functions etc., Science, Engineering and Technology. Many applications of Fractional Calculus