Fractional integration of the product of two multivariables H-function and a general class of polynomials

Abstract

A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, etc.). The main object of the present paper is to study and develop the Saigo operators. First, we establish two results that give the images of the product of two multivariables H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, multivariable H-functions and a general class of polynomials a large number of new and Known Images involving Riemann-Liouville and Erde'lyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, Mittag-Leffler function, Whittaker function follow as special cases of our main findings. Results given by Kilbas, Kilbas and Sebastian, Saxena et al. and Gupta et al., follow as special cases of our findings. © Springer Science+Business Media New York 2013.