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. |
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