Fractional differintegral operators of the generalized Mittag-Leffler type function

Dinesh Kumara,* and S.D. Purohitb

Fractional differintegral operators of the generalized Mittag-Leffler type function

Authors :

Dinesh Kumar^a,* and S.D. Purohit^b

Author Address :

^aDepartment of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur-342005, India.
^bDepartment of Basic Sciences (Mathematics), College of Technology and Engineering, M.P. University of Agriculture and Technology, Udaipur-313001, India.

*Corresponding author.

Abstract :

In the present paper we study a new function called as $R$-function cite{KumarKumar2014}, which is an extension of the generalized Mittag-Leffler functions. We derive the relations that exist between the $R$-function and Saigo-Maeda fractional calculus operators. Some results derived by Kumar and Kumar cite{KumarKumar2014}, Kilbas cite{Kilbas2005}, Kilbas and Saigo cite{KilbasSaigo1995}; and Sharma and Jain cite{SharmaJain2009} are special cases of the main results derived in this paper.

Keywords :

Fractional calculus, fractional differintegral operators, generalized Mittag-Leffler function, $R$-function.

DOI :

Article Info :

Received : April 03, 2014; Accepted : June 10, 2014.