Jñānābha‎, Vol. 50 (1) (2020), 164-178

GENERALIZED FRACTIONAL CALCULUS OF I-FUNCTION OF TWO VARIABLES

By

Dheerandra Shanker Sachan1 and Shailesh Jaloree2
1St.Mary’s Postgraduate College, Vidisha-464001, Madhya Pradesh, India.
2Samrat Ashok Technological Institute, Vidisha-464001, Madhya Pradesh, India.
Email:sachan.dheerandra17@gmail.com,shailesh jaloree@rediffmail.com
(Received : March 01, 2020 ; Revised: June 05, 2020)


Abstract

This paper is devoted to study and develop the generalized fractional calculus of arbitrary order for the I-function of two variables which is based on generalized fractional integration and differentiation operators of arbitrary complex order involving Appell hypergeometric function F3 as a kernel due to Saigo and Maeda. On account of general nature of the Saigo-Maeda operators, a large number of results involving Saigo and Riemann-Liouville operetors are found as corollaries. Some special cases also have been considered.

2010 Mathematics Subject Classifications: 26A33, 33C60, 33C70.
Keywords and phrases: Generalized fractional calculus operators, Appell function, Fractional calculus, I-function of two variables, Mellin-Barnes type integrals.