FRACTIONAL CALCULUS OF PRODUCT OF M-SERIES AND I-FUNCTION OF TWO VARIABLES   

By

Dheerandra Shanker Sachan1 , Harsha Jalori2  and Shailesh Jaloree3

1St.Mary’s Postgraduate College, Vidisha-464001, Madhya Pradesh, India 

2Government Shyama Prasad Mukharjee Science and Commerce College, Bhopal-462039, Madhya Pradesh, India 

3Samrat Ashok Technological Institute, Vidisha-464001, Madhya Pradesh, India 

Email:sachan.dheerandra17@gmail.com, jalori.harsha@gmail.com, shailesh_jaloree@rediffmail.com 

(Received: September 30, 2020; In format: June 19, 2021; Revised: August 14, 2021; Accepted: May 19, 2022)  

  DOI: https://doi.org/10.58250/Jnanabha.2022.52125

Abstract

The object of this paper is to develop the generalized fractional calculus formulas for the product of generalized M-series and 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. Again due to general nature of I-function of two variables and M-series, some special cases also have been considered. 

2020 Mathematical Sciences Classification: 26A33, 33C60, 33C70. 

Keywords and Phrases: : Generalized fractional calculus operators, Generalized M-series, Appell function, Fractional calculus, I-function of two variables, Mellin-Barnes type integrals