Asian Journal of Mathematics and Computer Research 12(4): 243-251, 2016 ISSN: 2395-4205 (P), ISSN: 2395-4213 (O) International Knowledge Press www.ikpress.org A STUDY OF SAIGO-MAEDA FRACTIONAL CALCULUS OPERATORS ASSOCIATED WITH THE MULTIPARAMETER K -MITTAG-LEFFLER FUNCTION RAJEEV KUMAR GUPTA 1 , BHUPENDER SINGH SHAKTAWAT 1 AND DINESH KUMAR 1 ∗ 1 Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur - 342005, India. AUTHORS’ CONTRIBUTIONS This work was carried out in collaboration between all authors. Author DK designed the study, performed the statistical analysis, wrote the protocol, and wrote the first draft of the manuscript and managed literature searches. Authors RKG and BSS managed the analyses of the study and literature searches. All authors read and approved the final manuscript. Received: 28 th April 2016 Accepted: 26 th May 2016 Published: 22 nd June 2016 Original Research Article ABSTRACT In the present paper, we study generalized fractional calculus operators involving Appell’s function F 3 due to Saigo-Maeda [1], to the Multiparameter K-Mittag-Leffler function defined by Gehlot [2]. Some elegant results obtained by Gupta et al. [3], Ram et al. [4], and many more are the special cases of our main established results. Keywords: Saigo-maeda fractional calculus operators; K-Mittag-leffler function; k-Gamma function; K-series. Mathematics Subject Classification: 26A33, 33C20, 33E12. 1 Introduction and Preliminaries The Multiparameter K-Mittag-Leffler function defined by Gehlot [2], as p K (β,η) m q,k [z]= p K (β,η) m q,k [a 1 , ··· ,a p ; b 1 , ··· ,b q ;(β 1 ,η 1 ) , ··· , (β m ,η m ); z] = ∞ ∑ n=0 ∏ p j=1 (aj ) n,k z n ∏ q r=1 (br ) n,k ∏ m i=1 Γ k (ηi n + βi ) , (1.1) where k ∈ R + = (0, ∞); a j ,b r ,β i ∈ C; η i ∈ R, (j =1, ··· ,p; r =1, ··· ,q; i =1, ··· ,m) and (i) if p<q + ∑ m i=1 ( η i k ) , then the power series on the right side of (1.1) is absolutely convergent for all z ∈ C, *Corresponding author: E-mail: dinesh dino03@yahoo.com;