GENERALIZED FRACTIONAL INTEGRATION OF THE (H)over-bar FUNCTION

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, et cetera). In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdelyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.